I know just how you feel. We have a right of way through our land and the absolute idiots we come across never cease to amaze me.
I do understand that people may not know why feeding horses (be it grass, polo mints, carrots or anything else) is dangerous- but the point stands that you don't need to know the ins and outs of equine husbandry to know that as they aren't your livestock it isn't your place to be feeding them anything. Just as I would not feed your pet or child- they aren't mine and I have no idea if what I might give them is safe or desirable.
The other thing I do not understand is why people cannot follow instructions they see on signs- warnings of electric fencing, signs asking people not to feed the animals or warnings that mare and foals should be left alone. The fact I have put up a double electric fence to try and stop people going in does not seem to deter some. I have actually had complaints from parents that their child was hurt by the electric fence, despite the signs warning of their presence and why they are there.
I caught one parent and two young children in the field (before running electric fencing along gate also) with a mare and foal- trying to catch and "pat`" the foal as it was cute. They were lucky the mare is generally quite laid back and an experienced mother- and even at that she was squaring up to them when I arrived. I hate to think what may have happened if I had been 10 minutes later.
I have also experienced people wandering into the yard to see the horses- through a gate, on private property. They go into the sheep and cattle pens sometimes too. Again to pet the animals. It's worse at lambing and calving time as the lambs and calves are small and "Cute" and also penned in.
Many people just don't seem t realise how defensive and dangerous animals- be it sheep, cattle or horses- are when cornered by people they are unfamiliar with and do not know how to handle them, let alone when it's a mother defending her offspring (as they see it).
The countryside and other peoples livestock are not playthings. They are living, breathing animals who deserve to be treated with respect. They can also be people's livelihoods.