You will probably be more informed about the weather if you Google "Vienna weather December" that in reading the replies you are going to get from people retelling their anecdotal experiences. Yes, it has been +10 Celsius in and yes it has been -10 Celsius in each place for days on end with sunshine, snow, freezing rain, etc..

What you need is the historical data so that the probability of a certain type of weather condition is something you are comfortable with.

As for cultural events, if you go to each city's touris information page there are "event searches" where you can select date ranges and type of event you are interested in.

Mahkeenac:
Here are some photos of snow in late March, in Prague and enroute to Telc (Teltsch). Freezing cold at that time of year, 25F, so you can imagine what December could very well be like. Did not in the least disturb our visit or the wonders of the city!
Stu

https://picasaweb.google.com/stuarttower/ScenesOfPrague#

Vienna, 1980's and 1990's:

https://picasaweb.google.com/stuarttower/Vienna1980S1990S#

well, here's my anecdote from late December in Prague, 6 years ago:

Cold, dry, sunny, with lots of people clearing the snow from the streets and pavements so there was no problem getting around.

We went to a puppet theatre, the opera, and a New Year concert in the Municipal Hall [great restaurant in the basement], and enjoyed them all very much. apart from the opera, we booked them all when we got there. there are lots of people handing out leaflets for concerts, so you should find plenty to interest you.

As for Vienna, we were there in summer and found finding out about musical events far more difficult. That was probably our fault for not doing our research well enough. WHat we did find was quite expensive; that would probably apply in winter as well.

Good luck!