Cocteau Twins do a really beautiful version of Frosty The Snowman and it's the only Christmas song I will play all year long. You can find it on their ultra rare "Snow" EP, but it also pops up on holiday compilation CDs as well. I remember seeing it on a Starbucks CD once.

Here's a cute video someone made for it and posted on YouTube.

http://youtube.com/watch?v=2P49MNDyf_Q

Cyndi Lauper also has a really sweet song called "Home on Christmas Day" which I love so much for the sole reason that it contains the lyrics...

"There's something about this season
That makes me feel a little queer
Everybody's so damn jolly
I wish you were here"

Here's her singing it live on Letterman

http://youtube.com/watch?v=A7PZalzFO8A