We were at Epcot for NYE. In the morning when the park opened, instant 1 hour wait for Fasttrack and Mission Space, but we just Fastpassed them. You could walk onto about anything else.
We left around 1:30 Pm to go back to the room to rest, and re-entered Epcot around 6:00 PM with no problems. The park was crowded but navigable.
We had dinner reservations at Rose & Crown for 7:20 PM. By 6:30 PM it started to get quite crowded in the World. As time approached the 7:30 PM fireworks show, it was stand still for the most part in England. After the fireworks, it loosened up, and around 9:30-10:00 PM you could walk onto Body Wars and most other minor attractions.