Hi there, Betty!
Walt Disney World definitely has days that are more popular than others, and New Year's Eve is one of those days. You'll find each of the theme parks generates quite a crowd, but because it's a smaller theme park,
the Magic Kingdom can reach capacity on holidays like December 31st.
Closures due to capacity are done in phases, so having an
advanced dining reservation can be a help if you are trying to arrive later to the theme park on a busy holiday. Usually, until they absolutely have to restrict the parks from accepting ANY more guests, those guests with dining reservations or appointments at something like
Bibbidi Bobbidi Boutique can still gain admission to a theme park.
I will caution you, however, not to arrive too late. Although it's very rare, there have been occasions where the Magic Kingdom has had to close to even guests with dining reservations. While the festivities at the other theme parks will help spread the crowd out, I'd say err on the side of caution, and plan to arrive as soon as you can.
Have an absolutely wonderful time ringing in the New Year in magical style!
Anna