No U Haul does not charger per mile for the use of trailers.
U Haul only charges per mile on U Haul Truck rentals so the farther you travel in the U Haul truck the more it will cost to rent the U haul Truck.
Also with a U Haul truck you have make sure you put more gas in the U Haul truck before returning it and it has to be at the level it was when you rented it.
You can however rent a U Haul trailer and pull it with your own truck or vehicle that is safely capable of towing the trailer.
Then you just pay the rental fee on the U Haul trailer and no additional per mile charges.
Then just return the trailer to any U Haul dealer in any state.