We visited Greece in late January because it was cheap to get there from Moscow, where we were living. There were a couple of cold days but most afternoons were sunny and relatively warm. If you like ancient sites without crowds, the off season is definitely the time to visit Greece. There were about 40 other people at the Acropolis the afternoon we visited, perhaps five at both Mycenae and Knossos, and no-one else was visiting Epidaurus or the Athens Agora. Athens’ usually touristy Plaka was quiet and charming.
Island-hopping is hard to do in the winter unless you have heaps of time. Boats leave Piraeus daily to most islands, but inter-island traffic is way, way down. The schedules are not set for more than a few days at a time, so it’s best to check with the tourist office the day before you want to go. Since the mid-winter months give tourist-industry workers a break, restaurants and rooms are usually closed in beachfront villages. Except for the occasional mail delivery, the boats that traverse the south side of Crete all summer stay in port for the winter. Some mountain refuges are closed, as well as some archaeological sites.