Anything is possible in this economy, but I wouldn't pin hopes or plan on it.
What WDW used to do until recently is charge you a rate based on when you checked in. So, for example, if you were going to WDW for two weeks starting on 11/15, whatever the room rate was on 11/15 was the rate you'd pay for each night, including Thanksgiving. And if it so happened that the day you checked in was MORE expensive than what it would be at some point during the trip, you were allowed to "break up" your vacation into 2 reservations, so when the lower rate began, you'd startt paying that rate. They'd warn you that, as a result, you may have to move into a different room for the different part of your reservation, but I've never heard of it actually happening.
However, they recently changed their reservation system so that, if they chose, every single day could have a different price for a room. Of course, they don't do that, but weekends are generally more expensive than weekdays, and if your stay brackets two traditional seasons, like going from Value Season to Holiday season, you will start paying Holiday Season rates when Holiday season began.
Again, don't anticipate discounts at all during Thanksgiving, so if they come, you'll be pleasantly surprised.