As a non-skier, I have spent several Christmases in ski resorts in Austria and Switzerland (because DH and sons love skiing and, due to dodgy knees, I can't).
It really can be a lovely holiday. Although we always stayed in hotels, not chalets, so I wasn't lumbered with any cooking or cleaning.
There are usually activities for non-skiers - spas, swimming, yoga, walks etc. You will probably find that there is a train to Saltzburg, which is a wonderful city to visit, especially in the Christmas season (Austrian trains are fast, comfortable and cheap).
The thing I loved most is that Christmas in Austria is so simple and traditional - none of the rushing around and commercial tat we have here.
I hope you give it some serious consideration, could be a once in a lifetime experience!