Map from Google - Cape_Verde

In Cape Verde the climate is very unusual, namely tropical arid, with temperatures generally not too high, despite the latitude, due to a cool sea current and the constant blow of the trade winds.
The islands are divided into two groups: in the north the Barlavento or Windward Islands (Santo Antão, São Vicente, Santa Luzia, São Nicolau, Ilha do Sal, Boa Vista), which have a more arid climate, and in the south the Sotavento or Leeward Islands (Maio, Santiago, Fogo, Brava), which are a bit more rainy. The northern Barlavento Islands are definitely desert, since they receive less than 100 millimetres of rain per year, while the southern islands receive between 200 and 300 mm of rain, so that here we can speak of semi-desert climate.
In both the groups of islands, in lowland areas or along the coasts, there are little rainfall concentrated in the period from August to October (and sometimes in July), which is also the warmest time of the year. The rains have an irregular pattern, which means that in certain years it can rain little or nothing, while in others there may be heavy rainfall, usually concentrated in a few days (or even just one); that may result in landslides and flooding, also because of the scarcity of vegetation, as occurred in September 2012 in Sal and Boa Vista.
In Mindelo, in the northern (Barlavento) island of São Vicente, less than 100 mm of rain per year fall, of which 45 mm in September.
Here is the average precipitation.
Average precipitation Mindelo
Mindelo J F M A M J J A S O N D Year
Prec. (mm) 0 0 0 0 0 0 0 25 45 20 5 2 97
Days 0 0 0 0 0 0 0 3 4 2 1 1 11

In Praia, in one of the Sotavento Islands, and therefore the rainiest, on average 250 mm of rain per year fall, of which 95 mm in August and 115 mm in September.
Here is the average precipitation.
Average precipitation Praia
Praia J F M A M J J A S O N D Year
Prec. (mm) 2 0 0 0 0 0 5 95 115 30 8 2 257
Days 1 0 0 0 0 0 1 8 7 3 1 1 22

As for the temperature, in the Cape Verdes there is a hot and muggy period from July to November, and a more temperate and dry period from December to June, during which the trade winds blow north-east steadily. During the cooler season, from January to March, the daytime temperatures are around 22/23 °C in the Barlavento islands, and around 25 °C in the Sotavento, while the night minimum is a few degrees lower, around 18 °C in the north and 19/20 °C in the south.
Here are the average temperatures of Mindelo, in the northern (Barlavento) island of São Vicente.
Mindelo average temperatures
Mindelo J F M A M J J A S O N D
Min (°C) 19 19 19 19 19 21 22 23 23 23 22 21
Max (°C) 23 22 23 24 24 26 27 27 26 26 26 24

The southern islands are slightly warmer, as we can see from the temperatures of Praia, the capital, located in the southern (Sotavento) island of Santiago.
Praia average temperatures
Praia J F M A M J J A S O N D
Min (°C) 20 19 20 21 21 22 24 24 25 24 23 22
Max (°C) 25 25 26 26 27 28 28 29 29 29 28 26

In Cape Verde it's rarely hot, however, the temperature can sometimes reach 35/37 °C from May to October, when the wind blows from the desert.
Even during the dry period, from December to June, on the northern slopes of hills and mountains, a little cloud cover can form, and a bit of rain or drizzle can fall. In fact, Cape Verde is an archipelago of volcanic islands, and in some of them we find mountains, among which Pico de Fogo, 2,829 metres high, in the island of Fogo, is the tallest: on the northern slopes of the island there is even a little greenery. On the island of Santiago, where the capital Praia is located, we find Pico da Antónia, 1,394 metres high, while in Santo Antao we find Topo da Coroa, 1,979 metres high, and Pico da Cruz, 1,585 metres high, and finally in São Nicolau there's Monte Gordo, 1,312 metres high.
The north-east trade winds begin to blow in November, and gradually lowers the temperature; the wind attracts enthusiasts of windsurfing and kitesurfing especially in the eastern islands (Santa Maria, Boa Vista), from November to May. When the weather conditions permit, the trade winds can turn into Harmattan, a dry wind that blows from the Saharan desert, and can bring dust and sand storms, reducing visibility and hampering human activities.
The amount of sunshine in Cape Verde is high all year round, but it's best between February and June. Between August and October, in the warmest and relatively rainy period, the sky may be cloudy for longer or shorter periods.
South of Cape Verde, in the ocean there is an area which is the initial part of the hurricanes' path; after they are formed, they move towards the west or northwest and head to the Caribbean. Some of these can touch the islands of Cape Verde, or they can directly hit the southern islands, although they are usually not strong, because they are still in the stage of tropical depression, and typically reach hurricane intensity when they're in the open ocean.

Cape Verde, Mindelo

The temperature of the sea in Cape Verde is high in summer, while it becomes a bit cool in winter, but still acceptable for swimming, as can be seen from the following table.
Sea temperature Praia
Praia J F M A M J J A S O N D
Sea (°C) 23 23 23 23 23 24 26 27 27 27 26 25

In the northern islands, the sea is slightly cooler in the winter months, when it drops to 22 °C.

When to go

Having a good climate, in theory, the Cape Verde islands can be visited throughout the year. But it is necessary to make some clarifications. Lively breezes often blow, so that it can be cool in the winter months, especially in the days when the temperature is lower, and those who are sensitive to cold could need a jacket, in addition the strong wind can make the water rough. This mainly occurs from January to March. Although there is often little rain even in the wettest period, from August (and sometimes July) to October, during which it may not rain for weeks, occasionally there may be torrential rains, although brief, so this period can be avoided for safety. Besides, in this period the sky is often cloudy.
So all in all you can choose the months of May, June, the first half of July, and November.
At noon, the sun is directly overhead twice a year, and it will stay nearby from May to September: care must be taken to sunburn, because the cool breezes can prevent from perceiving the intensity of the sun rays.

What to pack

In winter: light clothing, but also light scarf for the wind, sweatshirt or sweater, light jacket for the evening. To climb mountains, sunscreen, hiking shoes, sweatshirt and jacket for the evening; warm jacket and hat for Pico de Fogo.
In summer: summer clothes, a light sweatshirt for the evening, comfortable shoes for walking, possibly a light raincoat for August and September. To climb mountains, sunscreen, hiking shoes, sweatshirt and light jacket for Pico de Fogo.