We've been to HH for Thanksgiving many times and absolutely love it. But it IS a very different atmosphere than during the warmer months!
There are still lots of activities and people are in the pools, even if the air temps are a bit on the cool side. (The hot tub gets a LOT of use, too!)
If you're thinking of this year for Thanksgiving, I would make the call to MS right away to see if it's even still available. The resort is always at full capacity for Thanksgiving. From what I gather, you can usually still get a reservation at 7 months, but I don't know just when it fills up completely.
You can order a full Thanksgiving dinner through the resort as well. We've never done it (I do kind of a semi-homemade turkey dinner

), but people have said the food is very good. It's delivered to your room at the time you specify, along with instructions for re-heating.
Hope you get the reservation you want!