Horses sometimes will, yes, eat their own poop. Unlike rabbits, they don't do this as a routine thing.
They generally engage in coprophagy if they are not getting enough fiber or if their hindgut balance is off - after all, horses can't eat yogurt to fix things.
Poop eating can also be caused by a mineral or protein deficiency. Or just plain boredom.
Coprophagy is, however, normal in unweaned foals - it's believed that this is how they get their gut populated with good bacteria in the first place, by eating their mother's poop.