Makes sense but just FYI
The Welt offers very convenient, secure, and free underground parking. You just have to ask for passes.
Our plan when we went in the winter was to use this parking if it snowed. It is a nice backup plan. In fact we used it anytime we were in Munich because it is much easier to navigate than the tiny ramps to hotel parking in the area.
You might want to be flexible, considering how this winter has been thus far, you might end up having a 65 degree day and sunny to go run on the Autobahn at least. A jaunt down to eat lunch in Fussen and back would be well worth it IMO.