Budapest, Austria, Munich in December

Hi all! I'm thinking of doing a 12 day trip from Budapest to Munich through Austria in December with my girlfriend, who I hope to my make fiancée during this trip. I had some questions hopefully you guys can help with! I estimate I will arrive in Budapest on 23 Dec.

  1. How my itinerary looking?
  2. Should I consider other destinations since December will be cold with short days?
  3. I want to go snowboarding/skiing, where should I consider along my route?
  4. I want to propose somewhere with a beautiful backdrop, as I plan to capture the moment with a drone. Any suggestions? City/nature both work.

Itinerary:

Day 1-3: Budapest Day 4-6: Vienna Day 7-9: Salzburg, Hallstatt, Berchtesgaden, Gosau (Stay in Salzburg and rent car to get around?) Day 10-12: Munich

Interests: Natural history, castles, city exploration, outdoors, Christmas markets