OP
*if horses are such delicate animals then maybe it's not a good idea to ride them around behind a built up area where a lot cars drive through for a short cut to the main road.
We're near a hospital too so loads of ambulances and air ambulance can be heard throughout the day. What do the horses do then?*
My old horse was a complete school-master, you name it, he'd been there and got the T-shirt, so to speak. It's known as bomb proof. He could cope with tractors, lorries, double decker buses etc passing by him on the road without batting an eyelid. On the whole, he was good with noise (traffic, loud-speakers at competition, flapping bags stuck in bushes etc).
However, if some woman ran up behind him, shouting and carrying a small child I could not guarantee that he would not have been spooked and reacted accordingly. Even the most reliable of nags can get a fright once in a while, and generally something running up from behind them and screaming is more frightening than a noise or vehicle/object they will have gotten used to, such as large vehicles or vehicles with sirens.
Essentially, what you did, especially while holding a child, was very foolish and put yourself, your child, anyone around you, as well as the rider (not to mention the horse) at risk of being hurt.
I can understand you not being thrilled about the horse pooh near your driveway, though I think the salient point is that the horse didn't shit on the pavement or on your property, but on the public road.
You were totally OTT to shout. I have reported someone for doing something similar and they got some sort of formal warning from the police.
And horses do have the right to use public roads, including shitting on them. It's perfectly legal for horses and riders to be on the road, so long as they are obeying the highway code and not trespassing on your property or damaging it.
It's not a health hazard, unless you are planning on letting your child crawl through it and eat it. Older children can presumably avoid it if they wish to, what with it being so massive an eyesore.
I genuinely can't see why you don't understand it would be completely impractical to carry round a shovel and bag to shovel it up. And what where would they be tying the horse up so they could tidy the shit up? Or do you really think it safe to have an unsupervised horse on the loose? Just plain daft!