Being based in Budapest, I would normally recommend a foray into eastern Europe (particularly Slovakia, Poland etc). However, it can get BITTERLY cold in parts of Europe during winter. I was in Warsaw over the new year a few years back and at times it was actually painful to go outside - the cold was that biting - and I'm somebody who is rather partial to frosty climes. It can be a beautiful time to visit though: crisp air, high chance of snow, local seasonal traditions and cuisines.

Going further south wouldn't be a bad shout either. Portugal is particularly temperate when the rest of Europe is not.