Secretly sneak the snowman on top someone's back! A pass the token style game.
Paper snowman and tape
Players try to stick a paper snowman (make one from card stock with a loop of painter's tape to attach it) on a person's back without her noticing. When that person realizes the snowman is on her, she has to stick it on someone else's back. Don't worry about the snowman staying on just one back for hours -- giggling kids are sure to give the person a clue before too long. Try to have the snowman visit everyone's back by the end of the day.
For an extra devious version, have the person sing a Christmas carol before passing it along.