Except OP doesn’t seem to mind riders crossing, is the dumps that anyone with any sense would not want on their property, here front of the house, even if it was their horses that left them, I think?
Not being the OP’s horses, it feels the owners of said horses are the ones that should remedy the situation and find a solution, like hurrying the horses along there so they don’t dump.
We successfully did that with hundreds of horses for decades, is easy to do, or come back to clean the rare dump.
No one is expected to clean it all, just from their own horse.