It won't make any difference where you keep your chickens. It's your personal preference and what works for you.
The bigger issue is are they safe from predators? A horse stall is a great idea just make sure that nothing can dig under the walls and get into the stall. I have friends who didn't think anything could get to their chicks inside a 100% enclosed horse stall (made of wood). They lost several chicks one night to something that dug 10 inches down and under their wall.
Also, you want to keep the chickens away from all feed for your other animals. Don't let them get onto hay, etc. I keep mine covered with a tarp... inside my barn to keep my chickens from pooping on it.