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I'd say if possible, take your own boots. Skis are easy to rent and generally pretty good quality stuff.
You're pretty far from the Alps, but if I recall, there is a direct train to Zurich, and then it's a further 1-4 hours to the resorts in CH. You can also route through Frankfurt and Munich and be in Austria in 6 hours or so.
December is on the early side for the Alps, but there are a couple of decent snowfalls, not enough to get absolutely everything open and running. Still, the upper elevations are a safe bet. I personally like the Innsbruck area, it's got everything, not just skiing. The old town is compact and historic, there's an Xmas market, and easy public transport to the slopes, and a university.
While you're at it, don't forget to attend Oktoberfest, and you're really close to German wine country (the Mosel).