M.S.
You could do a twist on Pin the Tail on the Donkey. Make it Pin the Nose on Rudolph. Find a cut out of a reindeer and make a red nose out of construction paper. Use double sided tape on the back for it to stick, so there's no "pins" involved. Get a couple of plain scarves or handkerchiefs and use to blindfold the kids while they "Pin the nose on Rudolph." You could vary this in different ways. Such as pin the carrot nose on the snowman, pin the star on the tree, etc. Get a basket or something with small little rewards for the winners. Just a though. Hope this helps!