I guess everyones idea of crowds is different since we try really hard to visit off season....the week before Thanksgiving week is always quiet in our experience....we have been that week several times and always found it very empty. However the Friday evening before Thanksgiving the resorts really begin to fill up, by Sat the crowds have probably doubled at the parks and by Sunday it is very busy.
Once we stayed through the Monday before Thanksgiving and agreed that crods had easily tripled from the prior week (I would say Monday crowds are about like a mid June day....not impossible, but very heavy)