Good advice in the previous reply. Chance of a heavy snowfall is quite a bit higher in Dec than in Nov, though, for some cities (e.g. Berlin, Dresden, Prague), less of a problem for BUD or VIE or SZG.

As for christmas markets, the quality and charm varies tremendously by market (sometimes even in the same city). Many have become commercialized, little more than flea markets, with the traditional handmade christmas goods being hard to find (and expensive when you do find them). Big change in the past 5 years (mostly for the worse). But some are still excellent (Rothenburg and Dresden are 2 that come to mind). Salzburg is probably the quintessential december destination.