We went Jan 1 and 2 this year and it was CROWDED. Actually, DL wasn't too bad on the 1st when the park first opened but then it got crazy. But obviously, that was a holiday and it was also a thursday and friday so people were probably taking a long weekend. I would think that the 3rd and 4th being a sunday and monday shouldn't be as bad but I bet sunday will still be pretty crowded and maybe by the evening it might get better as people are starting to go home. I would think that Jan 4 wouldn't be too crowded since it seems like a lot of people would have to be back for school and work that day but you never know. Hope that helps. Good luck planning your trip!