I'm with Hunt. Don't over think it..
Back 20 years ago, I did a lot of NATRC competitive trail rides. The rules were everybody had to to tie to the trailer at night. My horses did well with that for years. I'd give them a hay net tied up high enough that they could not paw it or get a foot caught in it.
After a few years I bought some HiTies. They were great since they buffer any rope tugs. Made sleeping int he trailer with a horse tied outside a WHOLE lot easier. You didn't feel that constant tugging of the horse moving at night.
And Utah also has lots of places with no trees.
When possible I always high line at night. It gets the horses away from my trailer, so I sleep better.
I like to set the highline up where I can see it from the trailer windows. This allows me to look out at night and check on the horses
Some camp grounds have hitchen rails that I've used and my horses have done well with those
I frequently hobble my horses and let them graze during daylight hours. I've never trusted leaving my horses hobbled all night. My horses can run faster than I can even when they are hobbled. I've seen hobbled horses heading back down a trail and an hour later some camper looking for lost horses. They can hobble all the way back to the trailhead.
Some trail heads have corrals that are available on a first come basis.
And I frequently pull a hot string around a meadow and turn my horses out to graze. But again, I only do this in the daylight. I've had too many deer/elk run thru a meadow at night and knock down any hot wires
As you can see, there are all kinds of ways to contain your horses while camping, Your horses should be comfortable with all of these methods and allow you to choose the one that works best for the camp you are at.