OK, I'm retired military and have been to Germany over a dozen times since my last tour over there. A lot of people on this site don't grasp how different things can be with your advantages. First, I'd base out of the Edelweiss instead of Munich. The location and availability of things to do are that good. MWR can, and will, get you major discounts to any attractions, usually 20% often 50%. Use that service to visit the castles, Partnach, museums, Salzburg, and go skiing or sledding. They can also book reservations at local restaurants, provide transportation (included in all day trips, provide English speaking guides who are local and really know what's going on, and other services too. They can get you to and from all the castles, Munich, Salzburg, Innsbruck, etc...
Another reason to base out of there is you know you are going to have a good Christmas experience. They will be open, they will have the food and activities for travelers, and you're smack in the middle of a great, small, locality with some neat traditional customs you can take part in.
Munich is going to be shut down from noon on the 24th thru the 26th. Garmisch is not. I'd plan on skiing; MWR will provide everything including lift tickets, cheap. The runs are Olympic quality. There's also a huge spa and the Olympic swimming facility open.
As noted you will miss the main Christmas markets. But, if you take the tour to Oberammergau and Ettal on the 27th or 28th I'll bet you'll find plenty of stuff for next year. Salzburg will be fairly similar.
Neuschwanstein is neat for about an hour, Linderhoff is much better. If it's not clear I'd pass on Neuschwanstein entirely, as it's main draw is for pictures.
Expect snow or rain. Do indoor tours those days, or go to Munich or Salzburg. The weather can be very different a few miles away.