Seefeld, Austria - outside ice rink(s) - one artificial, skiing (downhill and langlauf), walking, sledge trips - unfortunately very touristy nowadays
http://www.seefeld.com/webcam/skz.jpgI think you've missed the skating course, but probably plenty of people around - even tuition. Other outside rinks in Leutasch and surroundings
Garmisch-Partenkirchen - 2 indoor Olympic-sized rinks, one outdoor rink, swimming pool, ski-jumping, downhill, langlauf. See the North Sea and the Zugspitze at the same time (the Nordsee, North Sea, is a fish shop chain and the Zugspitze is Germany's highest mountain - in the south)
Munich
http://www.eistanz-muenchen.de/Learn some Bavarian ice dancing - or go to the Olympic ice rink.
Enjoy the shopping, the Bierhalle, good food, wander round the Pinakothek art galleries, visit the English Garden (the world's largest city park I believe), take the train to Garmisch or Salzburg for the day.
Davos… or Arosa in Switzerland (expensive!). But if you think Switzerland's expensive, go to Sweden.