Agreed, the popular places definitely fill up in the xmas week. We've done this a few times now and usually book by mid year.I read earlier that you were considering Seefeld. Just a suggestion, you need to make some decisions soon-I looked at the Seefeld apartment we stayed at in June & it is booked out around Xmas. Booking.com says that they have 111 apartments like this already unavailable on their site (just fed in 20-23rd Dec as random to get an idea)
For an xmas stay, I wouldn't go with an apartment, as you miss a lot of the traditional Austrian White Xmas experience. I'd definitely recommend staying at one of the hotels with half board.
They put on a huge communal dining experience every evening with a special gala dinner on the 24th. They will likely trot in a brass band and carol singers, and they may even arrange a sleigh ride through the woods for guests.
Try shortlisting a few hotels and contact them through their website "contact us" page and ask for some dates. You can also ask to go on a waitlist, and they'll contact you with an offer if they get a cancellation.