Horse shit is mostly grass and other plants and doesn't really smell much. It will rain away or compost to dirt much quicker than smelly dog poop. But yeah, might be an idea to shuffle it out of the trail.
It's still shit. When I have to avoid it while biking or walking, it interrupts the tranquility of my enjoying the trail.
On a more serious note, a major problem with animal feces on trails that are shared with bikers is the risk it poses when you run it over, and it splatters all over the place. If it gets in your mouth, or on the nozzle of your water bottle or camelback, you can get sick.
Horse riders can always look back to a time when what they now do for sport used to be the only form of transit.
I come from a family of horse riders, and am a mountain biker. Really, it is completely possible to get along and share the trails. Obviously, some trails are only going to work for mountain bikes, and some are much nicer for horses (and boring for bikers).
I'd love to see horse riders required to clean up after their horses, just like dog owners clean up after their dogs. It's your pet, clean up.