In general, "de Europeans" put more effort into New Years than Christmas. If memory serves me correctly, the slopes will be open as normal on Christmas day, but service will be reduced on New Years day (lift operators & hangovers don't mix). Ditto for ski school - I'm pretty sure they don't do New Years day because they will be under the weather, but will do Christmas day.
We were in Zermatt last Christmas and while I wasn't able to ski at the time, I got the train up the mountain and met our party for Christmas dinner up the slopes. The restaurant was just doing 'dinner' - they had nothing special at all laid on for Christmas. This was a posh place and not a self service one which would do the same food day in, day out anyway.
We stayed in a Chalet with Inghams - flying from Belfast. The fact that the chalet was manned by UK staff meant that *they* put on a bit of a do for Christmas, so that might be worth considering. If you go to one of the more traditional hotels you run the risk that they either don't do anything at all for Christmas day or else they put on one of their gala dinners which last for *hours* and aren't quite as much fun as you might think. Of course, they will save the real celebrations for New Years Eve (St Sylvester, I think they call it in Austria) when there will be a serious party.
Inghams chalets might be a good idea - we found ours to be good value - I think it was something like £700 all in (over Christmas) which included your meals, wine at dinner, afternoon tea/buns, etc . . . It wasn't quite the James Bond sort of Chalet - this was much more functional, but given that most hotels in Zermatt were about twice that price this was just fine with us.
NB - lift passes (and ski school) in Zermatt were *savage* prices, so don't necessarily choose there.