I admit, that I am not only surprised by some of the answers given, I am totally shocked by the attitude.
I live in a reasonably rural area.
I ride down the road periodically.
When my horse manures in a place that is a rude place to leave piles of manure, I do go back after and clean it up. Sometimes that even involves tossing a muck bucket in the truck and driving there and scooping up the manure and driving home.
Manure just on the shoulder of the road not causing a problem is left. But for sure if my horse manures on the end of the driveway of someone (it has happened) I will make sure that is picked up as soon as I can. None of my neighbors should have to deal with the mess my horse makes on their driveway.
I think it is not unreasonable for the OP to ask here, we are horse people.
I also think it is not unreasonable for the OP to ask at the local barn where these horses likely come from that if they manure on the driveway could they please stop by after their ride and remove the manure from the drive.
The conversation with the barn owner will likely go best if you tell the barn owner that you have no problem with the riders, but please can they do something about the mess on the driveway.
???
What are you riding that you do not know your horse is manuring?