Horses aren't allowed on pavements. The same as bikes. Pavements are for pedestrians.
I must admit it would make life a lot easier for horse riders if we were allowed on pavements. A lot safer for us. But it would put pedestrians at risk.
Horses are allowed on roads, bridleways and shared use paths and tracks. The Trans Pennine Way for instance. They aren't allowed on Footpaths if it is just for people.
On privately owned land it is down to the land owner unless there is a bridleways through it. And then they must stick to the bridleways.
On council owned land it is down to the individual council. Where mine are kept they have blocked access to the massive council fields we used to ride on due to off road motorbikes using it.
A trailer is fine if you have one and want to box up and go hacking. But a massive PITA if you just want a quick hack.
Boxing uo involves hitching your trailer on (which might take 2 people), getting your horse ready to travel which may involve rugs, protective leg wear and a tail guard, loading your horse which might take 2 mins or 2 hours, driving to where you need to be, unloading and then undressing your horse, tacking up, securing your trailer and vehicle, go for your ride then reverse the process.
It's not like chucking your dog in the back of the car.
It is a hobby for most. The same as many other hobbies that may have an impact on other people. Football on a sunday morning takes up loads of fields and parking around here as does rugby on a saturday afternoon. Cycling can cause issues on roads. Swimming takes up council pools. Walkers use the countryside and can cause issues to paths. Keeping animals as pets can cause issues to others.
A bit of horse poo isn't really the issue. It's how intolerable some people find others enjoying themselves. No one owns the world, no one using that tow path owns it. They are probably there because either a charity or the council maintains it. Some people need to live and let live and be thankful that even in a large town there are green spaces that people can use freely.