I'm not sailing Infinity, but we have cruised over New Year's before... and going to be on the Golden Princess for New Years.
New Year's Eve is a wonderful night to be at sea. The ship does come alive. No one hiding in their cabins.
The two other times we've sailed New Years there was a deck party for New Years Eve, and all the lounges in the ship are hopping as well.
Enjoy your cruise and Happy New Years!