The decorations are something different than the Christmas events/parades. I believe that January 3rd is currently the last day for the Jingle Jungle Parade at AK, as well as the Osborne lights. So the other events will be wrapping up then (if not already done by the end of January), but then the decorations will start to slowly come down. I've been down there for the Marathon a few times. One year we saw just a few decorations left up while we were there. Another trip (2 years ago during their freak cold snap) almost everything was still up when we left, and they didn't get it all down til mid January.
So it depends on what day you arrive. You should see at least some of it, but I would definitely make it your priority the first few days if you want to see the Osborne Lights (awesome) or the Jingle Jungle Parade (meh) and then plan the rest of your trip after that. It is kinda weird to see the Christmas tree and decorations in the lobby of your hotel at night, and then when you wake up the next morning they are all gone.