We're leaving for BB in less than two weeks. However, we've been to BB twice this year and were there in mid-December last year, so as you can imagine, we're quite fond of it. Beautiful town, it keeps getting better and better.
The only thing we didn't like about our December visit last year is that the Caracalla spa was quite crowded. Lots of British families had come over on cheap Ryanair flights with their kids and *some* of them let their kids run wild...splash fights in the pool, talking loudly in the supposedly "silent" rooms (like one of the aromatherapy rooms). There were a couple of youngish adults who were also very loud (possibly drunk). So after that experience, we stuck to the lovely spa at our hotel, the Dorint/Sofitel. Much more relaxing.

Snow is unlikely in BB as well. It doesn't snow there very often.

I guess it effects what you pack, most of your choices will be cold (wet in Paris maybe). Might do better in French southern cities or Barcelona etc.

Also might be worth trying ski-de fond (cross country) as like walking but in snow ish

If you like the cold then it has to be Vienna, lots of museums, coffee houses, clean street food, shopping, trams, christmas markets with maybe day trips to Bratislava or Budepest for the spas