Having been in the World the past two NYE's, they do "close" the parks when it reaches "capacity". Generally this is in the noon- early evening hours. I would definitely pick your park, go in the morning and stay there....especially if that's MK.
I was in MK on NYE '99 and have to say, it wasn't nearly as crowded as I thought it would be. No more than, say, school vacation weeks. The only exception was on Main Street at the forecourt of the castle. A solid wall of humanity. Tip: don't EVER try to cross that with a stroller!! It took us almost 45 minutes just to get across. BTW, for those that were there in 99...how'd you like all the backup generators, lights etc?? Can you say, "prepared for the Y2k bug"?
And GOD!!! It was cold this past NYE, eh? We wore winter coats and gloves/mittens! DW and DD both got nasty colds and spent a couple days at "home". Two weeks later it was 70-80's.....after we left of course!