I've gone that first week for 3 years-last year I checked in on New Years Day! Never too crowded. Matter of fact, very slow. I remember having a conversation with a CM in Epcot about how quickly it seems to die down after New Year's Eve. She said that from what she's seen, a lot of people leave right away after New Year's. The biggest problem is the cold. I don't mind it, but be sure to bring a hat and gloves. One year on Enight, it was so cold, no one went on Splash Mountain. And another year, one morning was so cold that some of the shows in AK were cancelled or postponed.