I've spent several cruising New Years', mostly on Carnival. Even if it's not a formal night lots of passengers dress up. The ship provides hats and noise makers and weather permitting the party is up on deck with a countdown and a free glass of champagne. There are other smaller gatherings around the ship but the big one's on the Lido deck. It's pretty crowded but lots of fun with loud music and "happy" people lol.
Lyn