Yes Wanaka is already booked up - usually from the year before. It's a kind of "book before you leave last year" kind of place. Q'town and Te Anau are the same.
You might have more luck in Cromwell or Alexandra (Alex is v hot over Christmas) - or perhaps Naseby/Ranfurly...
Otherwise, if you fancy a bit of beach head down to the Catlins and either Owaka or Curio Bay. they're a bit quieter in that they don't have flashy restaurants and clubs ... really depends on what you are after.
Worse comes to worse, there are worse places to spend Christmas than toodling down to St Clair/Kilda beach each day (flat bit of Dunedin) or heading south a bit to Brighton beach.