As many have stated, horse poo is basically accelerated compost, unlike dog poo which is basically bacterial warfare. It's also worth noting it's not illegal for horses (and other wild animals) to poo on roads, and there's no requirement to clean it up.
From a practical point of view, it's a 50/50 chance whether you know a horse is having a dump. While some horses will stop to do the deed, many will carry on without breaking stride. It's actually surprisingly hard to see behind a horse, as the act of turning around will also turn a well trained horse (as you shift in the saddle) - that would be a bad idea on a road. Getting off would also be a bad idea - partly because to shovel the poo, you wouldn't be able to have adequate control over the horse; and partly because unless you're over 7 foot tall or incredibly flexible, you're going to have a hell of a job getting back on - even ignoring the fact that the "one foot in the stirrup and spring onto the saddle" works in films, but not so well in real life, unless someone is holding the opposite stirrup down (you're likely to spin the saddle, which is bad).
Bags are available for horses that are hitched to carts, and they're compulsory in most towns. Without a carriage you can't use them - you'd just have a bag flapping around a horse's back legs, which is not a good plan. The horse diapers are typically for monitoring horse health, not for riding - you can't do any more than a slow walk with them on, they fill quick and by god they're fiddly to get in place.
Why do people ride horses on roads?
Because inconsiderate idiots tarmaced, then started driving on the horse paths
. No one chooses to ride on roads, it's not fun in any way, shape or form - if you think cars are inconsiderate towards cyclists, try being on a horse. Unfortunately bridal paths are often split where roads run across them - if you see a horse rider on the road, they're just trying to get to the next path/field/stable, not popping to Tesco.
Don't you please think of the dogs and make the rich ******** clean up after thier horses.
If you think it's a rich person's hobby, you've clearly never been anywhere near a riding school
. It's only expensive if you actually own a horse, and even then that's only because of upkeep and stable fees - you could buy a good horse for less than you'd spend on a decent mountain bike. Most stables will have a stock of boots, helmets and body protectors to lend out, and you can ride in jeans and a t-shirt. Lessons typically cost between £10-20, and it's a great whole-body fitness sport - it's especially good for those of us with bad backs, because it improves posture and core strength. It's also surprisingly inclusive - a large number of physical and mental disabilities can be catered for.
