If you don't have a lot of winter clothes, at least go to wintersilks.com for some silk long underwear. I wore my "lightweight silk" ones the entire time we were in Europe last January.

There were some days (Florence) I wished I had gotten the medium-weight. But the trade-off is being too warm inside museums, restaurants, etc. Layering is key.

I've been to Vienna three times, ALL in January! The prices aren't any higher, and you might get snow, which makes the city so pretty. At any rate, the coffee houses are quintessential Vienna and prove to be a great way to warm up. The art and culture are great, as well as strolling the pedestrian streets (seeing all the local women in their fur coats!) I love the city so much I'm scheduled to go back for a 4th visit in Sept. I don't think I'll know what to do without the cold weather!

I've also been to Prague twice in winter (late December both times). It was hopping with people, and we saw snow (and no rain, I think).

London is also fantastic, so I think you really can't lose. In general, I think cities are fine in cold weather, as so much to see and do is inside (museums, churches, restaurants, concerts, etc.) I'd say pick what appeals to you most - 3 or so places for the 2 weeks - and you'll have a great time.