A singing contest just like American Idol but with Christmas carols
Karaoke Machine or comparable music
Out of all the people at the party, pick 3 people to be the judges. Have everyone perform a carol. The judges then pick whoever sings the best. And that person is declared Christmas Idol. Another way would be to have a twist. Tell the judges to pick the worst singer and that person gets a prize.
This game works better if you have a karaoke machine.