Many of the foreigners who live in Mykonos, Skiathos, Rhodes and Hydra rent their houses in the summer and return in September and stay through May and many of them will insist that it is the winter months hat they like the best. If you are an artist, poet or a person who can live on their thoughts a Greek island in winter can be like paradise. The island of Syros which is not dependant upon tourism has a rich atmosphere in the winter since the town of Hermiopoulis is the capital of the Cyclades and people come there to do business. Islands with large cities like Rhodes, Lesvos, and Crete are like cities anywhere. They don't close for the winter.
Life just changes.
People spend more time indoors, but the restaurants and cafes, bars and clubs are still open and on warm sunny days people still sit outside to eat and drink, at least in the day. The same goes for Athens. In my opinion Athens is a great place to be in the winter. When people ask me what they should do in Greece in February I tell them to base themselves in Athens and experience the nightlife of the city. Athens comes alive beginning in September and stays that way until summer with sidealk cafes full of people, restaurants supporting an army of live musicians and a clublife that rivals any city in America.