We went to Disney 11/16/02 - 11/23/02, which was the Sat-Sat BEFORE Thanksgiving. As far as crowds go, the parks were very light with literally no crowds by Disney standards. I think the longest wait time I saw was maybe 30 mins (ie, test track), but that wait was avoided by using fastpass. Weather was a little on the cooler side (mid 70's to low 80's), but that was to be expected. I must say though, from what I've read and heard, is that crowd levels increase from Thanksgiving week through the Christmas holiday. Therefore, if I had to choose I would choose the week before Thanksgiving.
PS - During our stay we even started to see Christmas decorations going up all over the resorts and parks !