Short answer
The Azores have a mild, oceanic climate with high humidity and frequent rain showers year-round. The saying about four seasons in one day is partly true: you can get sun, rain and wind within hours, especially in higher areas. Temperatures rarely go below 10°C in winter or above 28°C in summer. Pack layers and a rain jacket regardless of the season.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.