Petition horse riders to be under same laws and regulations as dog walkers

I would like to see horses and their riders being under the same rules as dogs and their walkers.
Dog walkers are required by law to pick up their dog's litter or otherwise face fines. I would like to see horse riders be under the same regulations when they are riding on public roads and parks because I believe that the effects can do much more harm than dog litter. In the worst case scenario horse faeces could close up the tread on vehicle tyres, possibly causing aquaplaining.
To enforce this, the rider or another member of the riding stables must search the route taken by the horse and scoop up any faeces that has been left.