Hi Carol - and welcome to the group!
I was just talking to someone the other day about this. My sister has been cutting my hair for over 20 years, but sometimes it is a year between visits to California to see her. I really dislike walking into foreign salons. I do Yelp and ask around, but it is rarely a good experience.
I think having someone in the park cutting hair would be awesome. I think I would feel more comfortable getting a cut from a fellow vagabond :) Obviously, mens cuts and ladies trims would be easiest. Coloring and treatments might be a mess with RV plumbing and such. However, I think you can do a decent business at the busier parks. Sure, the state requirements might have a learning curve, but who knows - maybe an underground outlaw gypsy hair salon might be in order!!
Good luck - keep us posted on what transpires!
kev