Map from Google - Argentina

Stretched over 3,700 kilometres from north to south, Argentina has very diverse climates, ranging from the almost tropical climate of the north, to the temperate climate of Buenos Aires and the Pampas, to the cold and windy climate of Patagonia, and finally to the subpolar climate of Tierra del Fuego. Besides, there is the cold mountainous climate of the Andes, arid in the north and central part, and cold and snowy in the south.
The rains are abundant in the north-east, while in the south-central, in the Pampas and Patagonia, there is a vast arid area. In the extreme south, snowfalls are frequent.
Being located in the southern hemisphere, in Argentina the seasons are reversed compared with North America or Europe.

Area with a subtropical climate
In the northernmost part of Argentina, the climate is subtropical, characterized by intense heat in the summer months, and nice warm temperatures during the winter months. In the western part, the Gran Chaco receives moderate rainfall, from 500 to 1,000 millimetres per year, with a pronounced dry period during the winter months. In Rivadavia, in the province of Salta, the heat is intense from November to February, with average highs generally around 34/36 degrees Celsius, and also with the highest peaks of all the South American continent: the highest recorded temperature is 48 °C! In winter the daytime temperatures drop to around 25 °C. However, the daily temperature range can be remarkable, so while it can get hot even in winter, sometimes it can get cold at night, especially when the Pampero, the cold wind coming from the southern lands, arrives here.
Here are the average temperatures of Rivadavia.
Average temperatures - Rivadavia
Min (°C)212119161211101114181921
Max (°C)363433282523242831323435

In summer, the rains occur in the form of brief showers, and are moderate from December to March, while in winter from May to August it almost never rains. Here is the average precipitation.
Average precipitation - Rivadavia
Prec. (mm)12011010055171063154080115671

Further east, in Formosa, the daytime temperatures are slightly lower, but the climate is much more humid and rainy: here 1,250 millimetres of rain per year fall, and it can rain even in winter, albeit less than in summer: in July and August, respectively 40 and 30 mm of rain fall on average. In the province of Misiones, east of Paraguay and of the Paraná River, the rains are more abundant, so much so that this area is covered by forests. At the Iguazu falls, nearly 2,000 mm of rain per year fall, while in Oberá the rains reach 2,300 mm. In this eastern portion there is no dry season, and the rains (which occur mainly in the form of downpour or thunderstorm in the afternoon or evening, and therefore do not affect much the sunshine amount, which remains good) are abundant throughout the year.
Here is the average precipitation at the Iguazu falls.
Average precipitation - Iguazu
Prec. (mm)1751751152001851551301251351802101351920

And here we can see the average temperatures.
Average temperatures - Iguazu
Min (°C)202019171311111213161819
Max (°C)323131272421222425283031

Iguazù falls
The Iguazu waterfalls are more spectacular in the January-May period, when the river that feeds them reaches its highest level.
To visit this northern subtropical area, since the main purpose should be avoiding the heat, which is torrid in the west and sultry in the east, you can choose winter, from May to August, keeping in mind that sometimes it can get cold at night, and that in the east there is no shortage of rain, and the sky may be cloudy as well.

Area having a temperate humid climate
In this area, which is located south of the Gran Chaco, and includes the estuary of Rio de la Plata, the climate is temperate, with mild winters and hot summers. Here the rainfall varies between 500 and 1,200 mm per year, summer is everywhere moderately rainy, because of afternoon showers and thunderstorms, while winter is rainy in the east, and drier in the west. It follows that the rainiest part, the one with no dry season, is the east, towards the sea and the border with Uruguay.
In Buenos Aires, the capital of Argentina, the average temperatures are reminiscent of places having a Mediterranean climate: the average in July is 11 °C, with average highs around 15 °C, while the average in January is 25 °C, with highs around 30°C. But in contrast with the Mediterranean climate, here it rains even in summer, in the form of afternoon showers and thunderstorms, which do not shield too much the sun. Also the changes in temperature are bigger than in the Mediterranean, because there are no obstacles both to cold air masses from the south (which may cause light frosts at night from May to September), and to warm air masses from the north, so much so that some days can be warm even in winter, with peaks of around 25/30 °C. In the capital, it almost never snows: snow accumulation occurs a couple of times per century. Rainfall is well distributed throughout the year: there are 9/10 days with rain per month from October to April (when as mentioned they occur mainly in the form of showers or thunderstorms), and 6/8 days per month from May to September.
Here is the average precipitation.
Average precipitation - Buenos Aires
Buenos AiresJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)12012515510590505565801401301051215

Regarding the temperatures, the best times to visit Buenos Aires are spring and autumn (October-November and March-April), but sometimes it can be very rainy: historically, the records in rainfall have occurred in March, April and October. All in all, the best time is usually spring, from late September to early December.
Average temperatures - Buenos Aires
Buenos AiresJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)201917141087910131618
Max (°C)302926231916151719232528

For swimming, the sea in much of Argentina is cool, because on the eastern side of South America, a cold current, known as Falkland Current, flows up to the latitude of Mar del Plata, where the sea temperature reaches 20 °C in February and 19 °C in January and March. It goes much better in Buenos Aires, where the sea is warm enough for swimming in January and February.
Sea temperature - Buenos Aires
Buenos AiresJanFebMarAprMayJunJulAugSepOctNovDec
Sea (°C)232322191613111011141821

Buenos Aires
In Rosario, 270 kilometres north-west of Buenos Aires, the weather is pretty much the same as in the capital.
In Cordoba, the average temperatures are not so different from those of Buenos Aires, because the city is located north of the capital, but farther away from the sea, and at 470 metres above sea level. Compared with the capital, here the diurnal temperature ranges are higher, and winter is definitely drier. The average temperature is 10 °C in July and 24 °C in January.

Arid climate
In this vast area, encompassing the western and arid part of the Pampa (north of the same line), and most of the Patagonia (south of the dashed line), the climate is arid, semi-arid or desert, because of both the distance from the sea and the Andean chain which blocks humid winds from the Pacific (in the southern part even the Atlantic coast is arid, because at these latitudes the westerlies prevail, and also because in the sea a cold current, which reduces the evaporation, flows). Clearly the temperatures vary with latitude, but some features remain similar: the temperature range between night and day is usually considerable (particularly at a distance from the sea); either cold or hot winds can sweep the vast plains, so that temperature variations can be considerable; the amount of sunshine is good in summer, while in the colder period, from May to September, the sky may be cloudy.
In Mendoza, 700 metres above sea level, at the foot of the Andes and not far from mount Aconcagua, the average temperature goes from 8 °C in June and July, to 25 °C in December and January. During the day the temperature may reach or exceed 30 °C even in winter, and at night the temperature can slightly drop below freezing from April to September.
Average temperatures - Mendoza
Min (°C)1818151163246121518
Max (°C)323127231916151820262932

On average, only 225 mm of rain per year fall, with a relative maximum in summer, between December and March. Here is the average precipitation.
Average precipitation - Mendoza
Prec. (mm)48383513841251381523223

Approximately south of the 40th parallel, Patagonia begins, most of which is located in this arid climate zone, but at this latitude the weather gets cool and windy, with strong winds that often increase the feeling of cold.
In Puerto Madryn, on the Atlantic coast, at a latitude of 42° S, the average temperature goes from 20 °C in January to 7 °C in June and July. In summer, there can be short heat waves with peaks above 35 °C. The sun often shines from November to March.
Average temperatures - Puerto Madryn
Puerto MadrynJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)13121175222571012
Max (°C)272723211612121517202327

Here it rains very little (just 170 mm per year), and in fact the landscape is semi-desert, with no trees, and only some xerophile shrubs. In winter, however, it can snow and freeze. Here is the average precipitation.
Average precipitation - Puerto Madryn
Puerto MadrynJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)161417111911151315171314175

In Puerto Madryn, the sea is cold: it reaches just 17 °C in February (so here it is not recommended to swim...), and drops to 9 °C in July and August.

Area with a subpolar climate
In the southernmost part of Patagonia and in Tierra del Fuego, the climate is cold oceanic, ie, with average winter temperatures close to freezing, and summer averages around 10 °C. Even precipitation, which at this latitude occurs often in the form of snow, resume growth, both because the Andes in the west are by now definitely low and therefore the moisture from the Pacific is able to penetrate inland, and because in this region even the cold and wet Antarctic winds can arrive. Winter is not too cold, because the cold winds which can at times lower the temperatures several degrees below freezing, are soon replaced by the westerlies, which are cold but not freezing. The almost constant wind, however, increases the feeling of cold. Summer, from November to March, is the best time to visit this southern part of Argentina: the temperatures are cool, even cold at night, but tolerable, at least when the wind doesn't blow.
In Ushuaia, located in a fjord at a latitude of 54 ° South, the average in June and July is just 1.5 °C, while in summer, the average reaches 10.5 °C in January. The night temperature can drop below freezing throughout the year, down to -1/-2 °C between December and March, and even -10/-15 °C from May to August.
Average temperatures - Ushuaia
Min (°C)65420-1-1-11245
Max (°C)1514121065569111313

Rainfall is frequent in summer, and snowfall in winter, although the amount is not high, around 500 mm per year. The sky is often cloudy. Here is the average precipitation.
Average precipitation - Ushuaia
Prec. (mm)303550505555456040353540530

In Tierra del Fuego the sea is cold all year round, as we can see in the following table.
Sea temperature - Ushuaia
Sea (°C)888877666677

Climate of the Andes
In the long Andean strip, the climate is progressively colder with increasing altitude. Of course, the more you go south, the lower is the temperature at a given altitude, and the lower is the height in which eternal snows begin.
The Andean zone can be divided into two distinct areas, separated by the dotted line on the map: north of the 40th parallel the climate is arid, while south of that line it becomes alpine, with abundant snowfall.

In the central and northern provinces, the Andes are desert even at high altitudes, in fact they are desert also in the western Chilean side, so there is no moisture which might pass over the ridges. In the north, above 3,000 metres, frosts can be intense from April to October, but during the day, when the sun shines, the temperatures goes above freezing: the daily temperature range is remarkable, because at high altitudes, at subtropical or tropical latitudes, the sun is very strong. You have to climb the rare peaks above 6,000 metres, like Nevado Queva, to find some snowfields, where the rare snowfall remains on the ground due to the cold.

At lower altitudes, the rains increase, because here the moisture comes from the eastern plain. In Salta, which is located almost at the Tropic, at 1,200 metres of altitude, 750 mm of rain per year fall, but it almost never rains from May to September, although at this time the sky is often overcast; rainfall occurs from December to March, usually in the form of downpour or thunderstorm, which doesn't shield too much the summer sunshine. Here is the average precipitation.
Average precipitation - Salta
Prec. (mm)18016512035934472665140755

The average temperature goes from 22 °C in January to 11.5 °C in June: so at this latitude, the climate is mild even at a low-mountain altitude, although at night it can slightly freeze from May to September.
Average temperatures - Salta
Min (°C)1716151274357121415
Max (°C)272725232019202323272828

In Argentina there are several very high peaks, among which Aconcagua, the highest mountain in the entire American continent with its 6,962 metres. At the latitude of Aconcagua (32° south) we find perennial snows above 4,000 metres, while in the area of Cerro Torre, around 49° south, eternal snows begin at 1,500 metres, although Viedma Glacier, which descends for gravity in the lake of the same name, comes down to just 250 metres. In the extreme south, the eternal snows are found above a few hundred metres.
At the latitude of Aconcagua, precipitation (which is more frequent in winter and therefore usually occurs in the form of snow) at high altitudes amounts to about 250/300 mm per year, like in semi-desert climates. You have to go to Patagonia, more or less at the 40th parallel south (indicated by a dotted line on the map) to find some greenery along the Andean slopes of Argentina.
In this area south of the 40th parallel, the cities located at the foot of the mountains are rainier than those located further east, where there is a desert: for instance, in San Carlos de Bariloche at 850 metres, 800 mm of rain (or snow) per year fall, while 200 km to the east, in Maquinchao, precipitation drops to 200 mm. Here is the average precipitation in Bariloche.
Average precipitation - Bariloche
Prec. (mm)2020305513514013011560402530800

In addition, at the foot of the mountains a downslope wind (called Zonda, similar to the Chinook of the Rockies or the Alpine Foehn) can cause rapid and abnormal increases in temperature.
The average temperature in Bariloche goes from 2.5 °C in July, to 14 °C in January.
Average temperatures - Bariloche
Min (°C)66421-1-1-1-1145
Max (°C)222219151076811141720

At Cerro Catedral, 2,400 metres above sea level and not far from Bariloche, the average temperature drops below freezing from June to September, and reaches 7.5 °C in January; the wind is often strong throughout the year. Snowfall during winter is abundant, but sometimes it can snow even in summer. In this area, the landscape reminds those of the Alps and there are renowned ski resorts, in which it's possible to ski when in North America or Europe it's summer.
In the southern Andes, there are vast glaciers and lakes of glacial origin, whose coasts have the shape of fjords.

When to go

You can not find a single period which is best to visit all Argentina, however, since to visit the extreme south you have to choose the austral summer, from December to March, you can choose this period for all the country, keeping in mind that at this time the north will be very hot. All in all, even November, a spring month, can be a good compromise for most of the country, although in the far north it can already be a hot month.

What to pack

In winter (June to August): in the north, Iguazu Falls and Gran Chaco, clothes for spring and autumn, light for the day, a sweatshirt or sweater and a jacket for the evening. In the north-central and Buenos Aires, warm clothes, sweater, jacket, umbrella. In Patagonia and Tierra del Fuego, very warm clothes, down jacket, warm hat, gloves, scarf, rain jacket, comfortable shoes. For the Andes: in the northern part, clothes for spring and autumn for the day, warm jacket and hat for the evening, sunscreen and sunglasses; in the southern part, warm clothes, down jacket, scarf, gloves, hiking boots.

In summer (December to February): in the north, Iguazu Falls and Gran Chaco, lightweight clothing of natural fibres, a light sweater and a light raincoat for thunderstorms, sun hat. In the north-central and Buenos Aires, summer clothes, a sweatshirt for the evening, possibly a light raincoat for thunderstorms. In Patagonia, clothes for spring and autumn, jacket for the evening, sweater, comfortable shoes. In Tierra del Fuego, warm clothes, sweater, raincoat, jacket, boots; be ready to remove the outer layer in mild days. For the Andes: in the northern part, clothes for spring and autumn during the day, warm jacket for the evening, sunscreen and sunglasses; in the southern part, down jacket, scarf, gloves, hiking boots.