To begin this game, you need a cardboard cutout of Santa. This can be purchased at some party stores, or even little gift shops. It doesn't have to be large, but it should be a big face of Santa. You can also find these at educational supply stores, or teacher supply stores, in the section of other cardboard decoration items that teachers put on classroom walls.
Once you get Santa's face home, cut off his beard. That's right, cut if clean off. There's no point in pinning Santa's beard on him if it's already there, right? The beard you sliced off can either be thrown away or keep it to tape back up later, if you want to use Santa's face for another game or as decoration.
Now, you can create several beards out of different items. It's easy to take a piece of thick cardstock and cut the beard out of that, or you can use foam with adhesive backing. You can simply peel the backing off right before it's used. You could also make the beard out of crumpled white paper, simply computer paper or the like. If you want to get a bit more elaborate, create Santa's beard out of cotton balls or a large piece of cotton pulled and shaped into the semblance of a beard.
If you have 5 people playing this game, you'll need 5 beards. 10 people? 10 beards. You get the idea.
You play "pin the beard on Santa" exactly as you play "pin the tale on the donkey" and similar games. Spin the person around, make sure they are blindfolded and then have them try to replace Santa's lost beard. Self-adhesive foam works well because once they place it on the picture of Santa, it's not going to move, so they can't change their blindfolded mind and change the position once they pick a position. It's there for the duration.
You can add several variations to this game. For example, you can buy a full-size cardboard Santa (again, the party stores often have these, or school supply stores, or you can make one of your own without much effort). You might have people pin the boots on Santa, pin the hat on Santa, or pin a red button nose on Santa.
Any good game offers a prize for the winner, and this one is no exception. You could always offer Santa to the winning "pinner" or you could have something more elaborate like a Santa goodie bag, filled with Santa pencils, Santa erasers, a Santa coffee mug, and Santa-themed candy.
More Christmas Ideas:
Little Kids Christmas Crafts
The Ultimate Christmas Guide
Christmas & Advent Celebration For The Holidays Package