Camping with my horses is regular activity for me. I did a lot of CTR early in my horse career. Since they judge you from when you arrive Friday afternoon until you leave on Sunday. Camping with the horse was part of the juding and I learned a lot.
You should be able to camp with your horses tied to the side of the trailer, to a highline, in a portable corral or forest service or ranchers permanent corral. We frequently sleep in the GN of the trailer. But depending on the time of year have set up smaller tents, large wall tents and some times just rolled the sleeping bags out under the stars.
My horses know how to hobble. I often turn them loose to graze in the morning and evening. I've learned that my horses will focus on eating for about 60 minutes. After that, they are looking to get into mischief. So as long as their heads are down eating, I let them graze, As soon as I see them looking around, I tye them back up. We often string a hot wire around a meadow to let the horses graze during the day. But we always highline at night. I don't like chasing horses back to the truck/trailer in the dark. I always keep one horse tied up. If I have to chase after the others, I don't want to do it on foot.
Here are two of my horses grazing while I cook breakfast.
I saw an old sheep rancher once, Who always carried a small nose bag of grain. He would turn his horse loose for lunch stops on every ride, When it was time to collect the horse, he shook the nose bag. He had trained his horses to come get their grain when lunch was over. He never had to go chase them. They always came to him.
Here some horse we hobbled during lunch. We turned them loose to graze with hobbles while we sat on a log and ate.
During the summer, there is usually enough natural grass for the horses to eat. But during the fall hunting season, I have to pack in hay cubes or pellets. Even if there is grass, I usually bring some hay or cubes to keep the horses occupied while they are tied up.