Map from Google - Sweden

Sweden is very extended in latitude, so that it has different types of climates: the subpolar climate of Lapland and the Scandinavian Alps, the Baltic semi-continental climate of the central and northern coasts (including the capital Stockholm), and the almost oceanic climate of the southern coast and islands.
Compared with Norway, the Swedish climate is usually drier and more continental, therefore colder in winter and warmer and sunnier in summer, because the westerlies, mild and humid winds which prevail throughout the year, are partially blocked by the Scandinavian Mountains, and are able to penetrate with some ease into the Swedish territory only in its southern part.
The Baltic Sea has a limited mitigating function, because it is a closed and not extended sea, especially in the north, where it narrows into the Gulf of Bothnia, which can freeze during the winter.
Here are the average temperatures in the capital Stockholm.
Average temperatures - Stockholm
StockholmJanFebMarAprMayJunJulAugSepOctNovDec
StockholmJFMAMJJASOND
Min (°C)-5-5-316111313951-3
Max (°C)-1-13916212220151051

Precipitation in Sweden is generally abundant: it is lower than 500 mm per year in Lapland, also because of the cold that lasts for many months a year, it hovers around 500/600 mm in much of the country, while it exceeds these values in the ridge of the Scandinavian Alps, where it can surpass even 1,500 mm per year, and along the southwestern coast, exposed to currents Atlantic.
In Stockholm, about 550 mm of rain or snow per year fall, so precipitation is not abundant, although it is well distributed throughout the year, and as happens even in the rest of Sweden, it experiences a minimum in spring, and a maximum in summer. Here is the average precipitation.
Average precipitation - Stockholm
StockholmJanFebMarAprMayJunJulAugSepOctNovDecYear
StockholmJFMAMJJASONDY
Prec. (mm)453025303545607560505550560
Days1086778910991011104

Winter is the season with the most noticeable contrasts, between the different parts of the country, but also between different meteorological situations: when Atlantic air masses move over the country, the temperature fluctuates around freezing in much of the country, at least in the plains, and may even exceed it in Stockholm and in southern regions, with rain replacing snow, but when the country is affected by Siberian air masses, the temperature drops across the country, to about -20 °C in the southern regions, and -40 °C in the northern ones.
Even the average winter temperatures vary greatly among different areas, in fact they are around 0 °C in January and February in the far south, -3 °C in Stockholm, -10 °C in the north-central part, and -15 °C in the far north. Consequently, even winter's duration varies depending on area, from three months in the far south, to nine months in Lapland. In Sweden, as in general in the Nordic countries, the winter is also characterized by the length of the days: in December the days are very short, and the sun doesn't even rise on winter solstice in the far north; February is typically colder than December, but the days begin to lengthen fairly clearly.
During winter, it often happens that almost all of Sweden is covered by snow, except the southern tip, i.e. the area of Gothenburg and Scania. In milder periods, in which the westerlies blow, the snow melts in a broader area, which often includes Stockholm, while the North remains permanently covered with snow.
In this satellite image we can appreciate such a situation, in which the south of Sweden is free from snow. Note also the sea ice in the northernmost part of the Gulf of Bothnia (Bothnian Bay or Bottenviken in Swedish).

Sweden from the satellite, snow cover in the centre-north

Summer in Sweden is usually mild or pleasantly warm, and it is the season of the year with the least differences between north and south. In the northern part, north of the Arctic Circle, in the Swedish part of Lapland, the three summer months (June, July and August) are the only ones in which the temperature rises steadily above freezing, with mild daytime temperatures, around 18/21 °C and sometimes even hot, while nights are still very cool, around 10 °C or below. On the other hand, the maximum temperatures are more or less the same throughout the country. This happens in the plains, because in hill cities, like Kiruna, which is located at 500 metres above sea level, the temperatures are slightly lower.
Average temperatures - Kiruna
KirunaJanFebMarAprMayJunJulAugSepOctNovDec
KirunaJFMAMJJASOND
Min (°C)-19-18-14-8-15761-5-12-17
Max (°C)-10-8-41714171482-5-8

Even the peaks of summer heat are similar across the country, around 28/32 °C; hot periods are typically short, and do not last more than two or three days.
In the western parts of Sweden, the temperature decreases with of altitude. In the Scandinavian Mountains there are several peaks above 2,000 metres in Lapland, while in the central regions they reach 1,800 metres. The ski season is longer than in the Alps, so much so that the final races of the ski World Cup are normally held in Sweden, in March (eg in Åre). Even the snowline is of course lower than in the Alps, thanks to the colder climate.
At lower altitudes, in the valleys among the mountains, summer is cool, also for the presence of the lakes, which are frozen in winter, and remain cool in summer.
East of the mountain range, there is a plateau with many cities at around 300/500 metres: here the winter is long and cold, and in summer the daytime temperatures hover around 18 °C, with cool nights, as we can see from the temperatures of Östersund, located in the central part of the country.
Average temperatures - Ostersund
OstersundJanFebMarAprMayJunJulAugSepOctNovDec
OstersundJFMAMJJASOND
Min (°C)-10-9-6-238101062-3-8
Max (°C)-5-305121618171260-3

In the southern part of Sweden, the coastline facing west, overlooking the straits of Skagerrak and Kattegat (see Gothenburg), has a wet climate, with skies often cloudy, and also windy, because of the prevalence of the westerlies, however, even here there are frosty periods and snowfalls in winter, when the winds blow from the east.
In Gothenburg, 670 mm of rain or snow fall per year, with a maximum in summer and autumn. Here is the average precipitation.
Average precipitation - Gothenburg
GothenburgJanFebMarAprMayJunJulAugSepOctNovDecYear
GothenburgJFMAMJJASONDY
Prec. (mm)503530403555858575656055670
Days1087879111111111112116

In the far south, even Scania (see Malmo) has a climate that shows the influence of the ocean, with average temperatures in January and February around the freezing point, and relatively cool summers; even here there is often cloudiness, wind and rain throughout the year.
Average temperatures - Malmo
MalmoJanFebMarAprMayJunJulAugSepOctNovDec
MalmoJFMAMJJASOND
Min (°C)-3-3-1271113121073-1
Max (°C)2251016202121171274

The island of Gotland, though less rainy and windy that the southern part of the mainland, has a relatively mild micro-climate, with an average winter temperature around freezing.

Uppsala
In the northernmost part of the Gulf of Bothnia (see Lulea), the sea is often frozen in winter, while it remains cold even in summer, since it reaches at most 14 °C in August.
Here are the average sea temperatures.
Sea temperature - Lulea
LuleaJanFebMarAprMayJunJulAugSepOctNovDec
LuleaJFMAMJJASOND
Sea (°C)0-1-1037131412852

The sea temperature in Stockholm, on the south-east coast, is close to freezing for a few months, while it reaches 16 °C in August.
Sea temperature - Stockholm
StockholmJanFebMarAprMayJunJulAugSepOctNovDec
StockholmJFMAMJJASOND
Sea (°C)3222510151613964

The sea temperature in Malmo, on the south-west coast, is similar to that of Stockholm, just warmer, and reaches 17 °C in July and August.
Sea temperature - Malmo
MalmoJanFebMarAprMayJunJulAugSepOctNovDec
MalmoJFMAMJJASOND
Sea (°C)32359141717151184

When to go

The best time to visit Sweden is summer, from June to August. June is the month with the longest days, with the midnight sun in the north and the white nights (midnight twilights) in the south, but July is the warmest month. From mid-August, the increase in rainfall and the decrease in temperature remind how soon the summer tends to decline at these latitudes.
In winter, the sea freezes in the north (see Lulea), while in July and August it reaches 13/14 °C. As mentioned, the sea temperature reaches 16 °C at Stockholm in August, and 17 °C in Gothenburg and Malmo: therefore it's a bit cold for swimming.

For those who want to visit Sweden in its winter look, in February the days are longer than in December and January, and in March there are still longer days and even warmer temperatures, although it's usually still below freezing, therefore with snow on the ground, at least in the north-central, while in December and January the days are very short. However, the more daring traveller may search just this kind of atmosphere, and maybe plan a Christmas trip to Lapland, with the omnipresent darkness, lightened at times by the aurora borealis.
Even for skiing, March is preferable to the winter months. In June, in the northernmost mountain resorts, you can even ski with the midnight sun.

What to pack

In winter: very warm clothes, especially for the interior and the north: fleece, down jacket, hat, gloves, scarf; for Stockholm and the south, you can add a raincoat or umbrella.
In summer: spring/autumn clothes, being ready to add or remove the outer layer, t-shirt, but also long pants, jacket, sweatshirt or sweater; raincoat or umbrella. Warmer clothes for the mountains.