Hello! I'm not sure but I've been searching for this myself as we'll be there too.
So HS is most likely to be up as they are showcasing JBJB and Flurry of Fun until the 6th. Hotels will start to go off by the 1st. MK will likely start to go off, but the castle will still be illuminated until the 6th aprox. (But there won't be a "castle lighting show"). As for AK, not sure but I've read that Epcot and AK are the fastest to go off, between Jan 1st and Jan 2nd.