We feel Jack Frost would fit in perfectly here as a spirit. In general, we like to leave most things up to the discretion of the player (ie whether or not people can see Jack) so that players are able to play their characters in a way that's fun for them. As a spirit, Jack would get to keep his powers as they're pretty nature-based anyway, and we see nothing wrong with Jack asking the wind for a ride, etc.

As for the moon, it's fine if you include the moon making Jack the way he is, although we prefer if you leave it as the moon and not Yue in particular. Since the moon gave a bit of itself to Yue to bring her from being a sick baby to being a healthy baby, when she grew up and sacrificed herself for the moon, she became a spirit. That's similar enough to what happened to Jack, so you're free to say the moon gave Jack a bit of its energy to pull him from the bring of death and make him what he is today. You can incorporate whether or not people need to believe in him/be spiritual into that history however you see fit.