No, they leave it on the insides of their blankets! LoL!
But, if you turn a naked, shedding horse out in an indoor arena, they will leave a hair impression which will sometimes startle riding horses later in the day, “OMG! It’s dead!” “It’s a pile of hair.” “Oh, I think not! That’s a horse that’s been steam-rolled to death!” “You are going to have to step in the hair sooner or later.” “I’M NOT GOING TO STEP ON A DEAD BODY!” and so on.
Mine went out for a couple of hours yesterday, in beautiful snow, after being cooped up on stall rest forever. Did she clean her sh!t-encrusted blanket? Nope. Too busy ordering everyone around (she’s the hall monitor of the little group of mares) to clean her revolting blanket. Why is her blanket so filthy? She spent her stall rest days going from hay feeder to window trying to both fill her belly AND keep an eye on her field, and occasionally yelling at them that they weren’t doing it right, “THAT’S NOT HOW YOU HORSE!” so she tracked her manure everywhere. Sigh. Apparently hall monitoring trumps tidiness and keeping one’s clothes neat.
At least she came in from the snow with blindingly white socks