March will be warmer than December (generally), although I cannot think of any specific March Munich events to attend or see? March is a good time to take the train to Garmisch-Patenkirchen and to spend sometime in the mountains walking, snow shoeing, or cross-country and downhill skiing.
Do not take the gondola up to the top of the Zugspitz. It takes 1 1/2 hours to go up, and then the same time to come down, when they are busy (during the winter due to ski season naturally), and once you get to the top there is not much to see that you cannot see from the top of any other mountain? And, it is very expensive (about EUR70-). If you are a serious skier, the skiing on the Zugspitz is pretty tame, and you can go elsewhere for less money and more pistes.
Unique Suggestions: If you are going to go...
The train from the Hauptbahnhof runs every hour and takes about 1 1/2 hours to Garmisch. The cost is EUR14 for a one way ticket. From the train station in Garmisch, you can take the Zugspitzbahn. Just walk under the train tracks, away from the main station, and at the end of the tunnel you will see the Zugspitzbahn station on the left hand side.
Fun Alternatives: You can use the Zugspitzbhan to reach the Hausberg and Oesterfelder gondola stations. At the Alpspitz they have just installed new high speed gondolas to service the Kreuzeck.
Continue on in the Zugspitzbahn and you will reach Grainau and the Eibsee. If you have a valid ski ticket you do not need a separate ticket for the Zugspitzbahn.
Garmisch-P is a resort town and therefore has resort prices in its shops. I would do your shopping in a bigger town where things aren't so overpriced.
Unique Suggestions: This being said, it doesn't hurt to join the locals and go window shopping on a Sunday afternoon.