I've never actually braved the crowds on New Year's Eve, but conventional wisdom is that you would have to arrive pretty early. Probably right around opening time. I wouldn't arrive much later than an hour or so after opening. This tends to be one of the most crowded days of the year at the park and it is not uncommon for them to close the gates at some point. If that happens, you would have to stay inside the park for the day, as I don't think they let people re-enter once the park is deemed full.