I live in Germany.
To echo what others have written already, you are likely to be spending most of your time in southern Germany, so it's very simple to cross the border into Austria, Switzerland, and just a bit further over the Brenner Pass into South Tyrol (Italy). The Arlberg is simply awesome, I also recommend basing yourself in Innsbruck, Austria, and taking advantage of the easy transportation to the nearby resorts (Nordpark, Axamer Lizum, Stubai Glacier, etc.). In many of these cases, the ski buses are free of charge from downtown Innsbruck during the high season. Innsbruck is just under 2 hours from Munich central station by train.
With a car, you of course have more options within convenient reach. If you're relying on trains and buses, it's still pretty easy, but keep in mind that you're probably going to be hauling a fair amount of gear around.
Within Germany, the main choices are the Garmisch area, Oberstdorf, and a nice little spot called Spitzingsee/Schliersee. At least those are the places I've been to, all are nice in their own way, but somewhat smaller than the large resorts in Austria. Garmisch I personally found to be a bit too spread out and difficult to properly schedule from the center of the city (~40 minutes to the Zugspitze summit, with poor schedule coordination between the transportation options), but the view is to die for.
And then return to Munich for a few days, to drink the beer!
More info, just send me a PM.
