Cold is no problem. Empty is a feature, not a bug.
(There will be places to stay and restaurants open on Santorini - just not all of them.) It will be warmer than NY, almost certainly. Wet and windy is typically a miserable combination, but it really depends on whether it's incessantly wet and windy, or instead there are just a few stormy days on which you'd rather just sit inside by the fire but most of the time the weather is fine for outdoor activities.
For those who've sampled both climates: how does Greece's weather in winter (particularly the islands and the Peloponnese) compare with that of Northern California or coastal Oregon? I have to say, I love that region's weather despite the rain - or, perhaps more accurately when thinking about tourist activities, I love that it doesn't typically rain incessantly and usually there will by at a few not-rainy (if not outright sunny) days for every rainy day.