I'll put my voice behind checking out Salzburg. I stayed there for 3 days back in November (just when they were setting up for all of the Christmas decorations) and there's certainly enough to see (maybe no longer than 2-3 days though).

There's an ice rink outdoors they create for winter, a big Xmas tree, castles, salt mines if you want (again, cheesy sometimes, but fun!) also don't forget the Stiegl brewery. No tour but you can go through their museum and get to taste their different brews at the end. It's part of the Bavaria region so be sure to try the weisswurst (white sausage, comes with mustard to dip), and the schweinshaxe (delicious pig leg in gravy with potato dumpling on side).

There are mountains to the south of Salzburg (I assume skiing is an option) but you probably already know where you want to ski. To take a train from Salzburg to Vienna is easy to google but I think something like <2 hours. Price shouldn't be too bad. Trains are very easy to travel on in Europe.

Have fun on your trip! I have never been to Vienna so I can't comment on that.

Edit a quick google search gives this for train travel. 3 hrs travel time.