I can't swear to this information but we were there three years ago and were told that if your staying on property and have a multi day park
hopper pass that you've already been using then you will always be admitted to a park.
Oldest DD and I were at NYE at MK 2000/01 and DH and I were at Epcot this past NYE (2002/03).
I don't remember if we got anything under our door at the resort this year, but the year DD and I went, there was an information sheet put under our door when we got up the morning of NYE day. What I remember it said was what is stated above, but the trick is that you will be admitted to
a park, not necessarily the park of your choice. It said if you wanted to make sure you got into a specific park, to get there by noon and stay at that park. I don't think that is important if you plan to go to Epcot, but it is if you are planning to go to MK or the Studio, which have smaller capacity.
The year DD and I went, I know that MK closed to all guests at some point. The next day, we heard people talking who had gotten on a bus that was supposed to go to MK. On the way there, the bus driver got a message that it was full and their bus was diverted to Epcot. We got to MK about 11am. It was crowded, but still lots of fun. There were extra shows and bands on the stages, a regular Spectomagic parade in the evening and then the fireworks at midnight that were shot off from all parts of the park, not just Fantasyland. Really cool.
Last year, DH and I went to Epcot. There was entertainment in each country (bands, DJs). It was not very crowded at all. We ended up leaving to walk back to YC about 7 because it was pouring rain. Even with ponchos we were soaked. We planned to go back to the park later on, but never did (It's hard to go back out in the pouring rain once you are in a nice warm, dry space). The rain didn't really let up until about 2am, so crowd estimates from last year are probably not the usual. We did hear though, that Epcot almost never closes due to capacity on NYE.