NYE is like nothing you have every seen before. Wall to wall people. Traffic jams getting in. Full parks. Full lots. Only exception is AK which is the least crowded.
This past year on Dec 31, we did EPCOT early for a few hours and then hopped to AK for the afternoon. We stayed out the parks at night and did hoop dee doo review instead (kids were 8 & 7 and not late night kids anyways). We stayed away from the crowds for the most park except for some extra vehicle traffic.
We have done early mornings on Jan 1 the last few years and it's actually not too bad for the first few hours I guess due to lots of people having late nights.
As already noted, this is the busiest time of the year. It's still going to be crowded Jan 2,3,4 through the weekend.