You just have to watch where you're going, but horses are far more durable than most people think.
Wednesday morning as it was coming daylight we left the corrals in single file through mesquite, down through draws, coolies, and washes. There were 10 of us and the herd boss was leading the way, because he knew the area.
I was next to last in line, and I hope I never forget the look in front of me. We were traveling at a fast trot and it looked like something out of a movie. Even at 73 I still like the company of those kinda folks. They all know horses, and cattle, and we all knew what we were doing.
A country music film crew was filming us with drones at that point, and then with their big shoulder carried cameras around the corrals.
When we got all 330 head penned we tied our horses to the corral fence. They were all soaked in sweat and steam was coming off of'em as it was still pretty chilli, and the video crew filmed that to.
If I find out what music video we were in I'll post it.
But back to your question. Sure the horses get stickers, and thorns occasionally, but you just have to keep checking em. Horses hide is pretty thick, and tuff.