We've been once before the week of Thanksgiving and are going back again this year.
The parks weren't too bad early in the week. Every day it got a little bit busier. It was pretty crowded Thanksgiving and Friday, but we had seen everything that we HAD to see earlier in the week, so we were really just circling around to see the things we wanted to see again.
The temps are usually in the upper 70s, so the weather is nice. You see whether you go to the waterpark based on the weather report. But it can get outright cold in the evening.
For us, we won't go in the summer because of the heat and humidity. We don't vacation well in that kind of weather. I also won't go Christmas or Spring Break because of the crowds. So Thanksgiving works well for us. We only need to pull our kids out of school for a couple of days, the weather is usually cooler (which has it's pros and cons) and the crowds didn't seem that bad to us.
Just make sure you make your Thanksgiving dinner reservations as soon as you can. The popular places sure filled up quickly this year.