I've been to Brown County and know the area you're talking about - in their defense, that's just one loop of the horseman's area with all those walnuts. That's also kind of "part of camping." You know, being outside. . .in nature. . .and all the stuff that falls out of it.
Just make a mental note not to camp in that section of the campground during the time of year the walnuts are dropping. The other times of the year, it's one of the prettier loops - nice and shaded, too!
As for horses sleeping in the trailer - not something I'd do, personally, but only because we have two horses and a two-horse slant. . .after a long day of riding, I don't want to lock my horses up into what is basically a metal "standing/tie stall" all night. Even with the windows open, the ventilation isn't as good as it could be outside.
I'd just take my chances with the walnuts and keep the horses outside where they can turn, move around, stretch out, lie down, get a drink of water, and rest up for the next day.
"Parelli horsemanship is just like painting by the numbers. You need absolutely no skill. You just put this color here and this color there, and when you're done, you have ... a mess no one wants." mp