The only issue I encountered last NYE was traffic!! But it shouldn't be a problem if you're not driving. Some main roads were blocked off for the races & I couldn't even get to Magic Kingdom during the day. I went to Epcot by default, but left well before evening. We spent the evening at our hotel(Port Orleans), ate a delicious meal at Boatwrights, & partied with Mickey. The resort was giving out hats & noisemakers & had special activities planned. And we hit the uncrowded parks first thing the next morning!
PS- for anyone driving, the resort parking lots are FULL during this time!!