Are there any palm trees that grow in zone 6? What kind?

Answer 1

Temporary ones.
I'm not really being totally sarcastic. I know someone who has friends with a greenhouse. He keeps a palm by his pool and then moves it in a truck to their greenhouse for the winter.
They don't cost a lot, in Florida. I have toyed with the idea of bringing one back in my van and planting it in the spring, and just letting it die.