Typically the Tuesday and Wednesday after Thanksgiving DL closes earlier (I think around 6 if I remember correctly, instead of 8) for the Cast Member Christmas Parties. Each year they hold 4 cast member parties. 2 parties are called Mixins. They're usually held the Sunday before and the Sunday after Thanksgiving. These parties give Cast Members and their families all day passes to both parks, plus extras perks to CMs and their families on those days. So there will probably be a lot more CMs running around on those days.
The tuesday and Wednesday after Thanksgiving is usually the 2 private parties. When exiting the park you will see hords of people lining up to get in. It's so funny to see the confusion on guest faces as we all watch them leaving in the park. Here you will probably encounter the biggest crowd of the day. Guests must walk around all of us standing at the gates waiting for the party to begin.