This might be a little over the top for a holiday party, but we're charmed by the idea of printing an invite on a hanky. A friend forwarded us the picture above (she was hunting for ideas for her wedding).
It would certainly cost more than paper invites, and it would involve way more time; however, think of the delight your guests would get when opening the envelope.
You could do the same thing on tea towels. Then your invite also serves as a gift, you're skipping the paper which will get tossed in the trash eventually, and you're giving something that could hopefully be used again and again in place of a paper product.
We're over-thinking it now.
All in all, it's just a cute idea.