IMO I would say you HAVE to go to see Nurnberg's Christmas Markt. I also really like Erfurt's (former DDR/GDR) and Dresden's markets. Some other nice Weinnachts markts in the area are: Munich, Salzburg, and Rottenburg.
Perhaps this might get you in the mood...
German Christmas Markets...
http://www.1addicts.com/forums/showthread.php?t=467893
and here is
Nurnberg's Christmas Markt...
http://www.christkindlesmarkt.de/english/
And yes... it is wintertime over here... your rental car needs winter tires. Snow or no snow, it is cold out and we have black ice and slippery roads in the mornings. German law says IF you get into an accident and you don't have snow tires on (M+S plus you need the snow-flake symbol!) then you are found at fault. AND... your insurance might not pay for any damage. So... all Germans buy and mount thier snow tires since Oct 15th until April 15th.
Have fun durring your stay.