Christmas somewhere in Europe on a shoestring?

Hello all. I wonder if anybody would be able to advise? I'm looking to escape the impending misery of British winter for at least a week of it, but unfortunately lack the necessary funding to go further afield than Europe. I'd ideally be looking to go over the Christmas period (say for a week like 21st - 28th December or something similar). Is this feasible? Are hostels generally open over this period?
Any good (and cheap) suggestions of where to go and what to do, even if it's not over Christmas, would be gratefully received. Ideally I'd like something warmer than it'll be here, but anything cheap and good and snow-related might also be fun.
Thanks all.

Thanks for the reply! I wouldn't have thought of Romania, I'll have to investigate. For snow fun did you have any particular recommendations? I hear Poland can be good? Of course the problem there is that any saving I make on going to eastern europe will be probably more than countered by buying proper winter clothes! Frustrating. Athens is a little more expensive, as you'd expect I suppose. Can't make an omelette without breaking eggs I suppose.
Anyway, thanks for the response, I look forward to hearing more (hopefully).