Answer:
I don't believe so, unless the government printed them and distributed them, I don't think they are.
Correction
They are novelty items that sell for a couple of bucks but have as much purchasing power as the paper they're made of (i.e. none). The U.S. has never printed special Christmas currency or minted Christmas coins for circulation, only stamps.
Correction
Santa dollars are real one dollar bills with a sticker of Santa's face on it. You can peel it off and you will see George Washington's face underneath. They are genuine, legal, bankable, and spendable. It's worth a dollar but as a novelty item it's worth about $10-$20. You can check them out at www.santadollars.com