I disagree with staying on the mainland. They can get snow in Athens you know.
Ferries are indeed a problem but there is no problem with flying to one of the larger and more southern islands. Rhodes and Crete would be the obvious choices there. It can be 20C with blue skies and sunshine on either on Xmas day. I know, I've experienced it. The average however is more like 12-15C Both can offer scenery and hiking. To find vegetarian food is never a problem in Greece. It is one of the birthplaces of vegetarianism you know. You'd have a much harder time finding things to eat if you were a vegetable hater. LOL
https://www.urbanadventures.com/blog...de-athens.html
As a confirmed meat eater, my diet when I lived in Greece became much closer to vegetarian than I would have believed it could be. I wish I could find a good spanakopita (spinach pie) where I live now. It was one of my favourite quick lunch time choices and I hated spinach as a kid!
I would say weatherwise, you can expect more middle California weather on either island. Yes it could rain for your entire stay but it isn't that likely. Also, when it does rain it tends to pour down for several hours and then stop. So looking at average rainfall numbers can be misleading in terms of will it rain all day.
Santorini is not an island I would visit in winter. Frankly, there is nothing much there beyond the scenery and the tourism it generates. The bigger islands farther south give you much more scope to work with in all ways.