Vienna offers several christmas markets, the best known and most crowded is the one on Rathausplatz (in front of city hall). A very neat market is placed in the 7th borough in the "Spittelberg" district. Mood in Vienna is awesomely nice (although most residents and car owners hate it) if the city gets covered by snow. Unfortunately snowfall has become a rare event, but January and February often bring the white gold to Vienna.
Markets are mainly visited for hot beverages like mulled wine or glogg (with much rum!) leading to weird actions in the late evening.

December is perfect to visit museum or concerts, weather can be very dull.