Map from Google - Madeira

The two islands of Madeira and Porto Santo, which belong to Portugal, have a very mild climate, so they can be considered as the islands of eternal spring.
The north-east trade winds, which prevail throughout the year, bring a little cloudiness, humidity, and rainfall in the north facing slopes. On the other hand, during the winter, the country can be affected by Atlantic disturbances.
The daytime temperatures hover around 19/20 degrees Celsius (66/68 °F) from December to April, and above 20 °C (68 °F) between May and November, reaching up to 26 °C (79 °F) in August and September. The minimum temperatures hover around 13/15 °C (55/59 °F) from December to May, and around 17/19 °C (63/66 °F) from June to October.
Here are the average temperatures of Funchal.
Average temperatures - Funchal
FunchalJanFebMarAprMayJunJulAugSepOctNovDec
FunchalJFMAMJJASOND
Min (°C)131313131517181919181614
Max (°C)191920202122242626242220
Min (°F)555555555963646666646157
Max (°F)666668687072757979757268

The sea temperature is not very high, in fact it ranges from 18 °C (64 °F) in winter, to 20 °C (68 °F) in June, and 23 °C (73 °F) in August and September.
Sea temperature - Funchal
FunchalJanFebMarAprMayJunJulAugSepOctNovDec
FunchalJFMAMJJASOND
Sea (°C)181818181920212323222119
Sea (°F)646464646668707373727066

Rainfall is concentrated in the cool season, from October to March, when it's quite frequent, while in summer it almost never rains. The island of Porto Santo is more arid than Madeira, and its landscape is green only in the northern inland area, where the altitude reaches 500 metres (1,600 feet). In the city of Porto Santo, the annual rainfall does not reach 400 millimetres (16 inches), while in Funchal, the capital, located in the island of Madeira, it's around 640 mm (25 in).
Here is the average precipitation in Funchal.
Average precipitation - Funchal
FunchalJanFebMarAprMayJunJulAugSepOctNovDecYear
FunchalJFMAMJJASONDY
Prec. (mm)1058565402012333575100100640
Prec.(in)4.13.32.61.60.80.50.10.11.433.93.925.2
Days1211108531269111391

The amount of sunshine in the two islands is acceptable even in winter (with about 5 hours of sunshine per day in November, December and January), while it's good (but not great) in the summer months (reaching on average 8 hours per day from July to September, for example the Canary islands experience more sunshine in the same period).

Madeira

The island of Madeira, the largest and occupied by higher mountains, whose highest point is Pico Ruivo, 1,862 metres high, hosts a greater variety of microclimates, due to the above-mentioned trade winds: the northern side is more rainy and windy than the southern, where the landscape is more arid; the city of Funchal, on the southern slope, is quite sheltered from the winds. On the other hand, the interior, which is hilly and mountainous, can be covered by a layer of fog or low clouds. Of course, the temperatures decrease with altitude.
In the period from June to September, Madeira can be affected by the Leste, a hot dry wind blowing from the Sahara, which can raise the temperature above 30 °C (86 °F), and bring a fine red powder. This wind is more rare in Porto Santo.
In June, a blanket of cloud (called capacete) that covers the island of Madeira in the early morning, but thins out during the warmest hours, often forms.

When to go

Having a very mild climate, Madeira and Porto Santo can be visited throughout the year, but from mid-October to mid-April there may be rains and thunderstorms, especially in the island of Madeira. For swimming and sun bathing, the best time is summer, from June to September, even though in June the sea is still a little cool, while the fans of nature and flowers will appreciate spring.

What to pack

In winter: spring/autumn clothes, sweater, jacket, raincoat or umbrella. To climb Pico Ruivo, down jacket, hat, hiking shoes.
In summer: light clothing, but also a scarf for the wind, a sweatshirt or sweater, a light jacket for the evening. To climb Pico Ruivo, sunscreen, hiking shoes, sweatshirt and jacket for the evening.