Horse riders and their mounts regularly suffer from the same thing as we do, including getting killed. I think it may be more helpful to join with them rather than let drivers divide and rule us. Though it does cost some money to buy and keep a horse, it honestly isn't only toffs that do it. It costs about the same for a DIY livery (what most people have) as running a car, and a decent ordinary horse would cost about 3-9 grand, though of course you can pay less, or very much more, if you want to. There are more horses in the UK now than before the car was invented. Not all those owners are toffs.
Drivers are sometimes aggressive to horses/riders because
they see them as toffs. It's not a helpful stereotype.
The equivalent of the CTC, the BHS, has a page in its website for reporting incidents (including an interactive map) because they find it as difficult as we do to get the authorities to take incidents seriously. Many riders I know dare not ride on the roads any more because of the overt aggression they get from drivers.
Drivers under-estimate the width of a horse+rider, just as they do the width of bikes. A friend of mine had a van smash into her stirrup, breaking it in half, damaging her leg and terrifying her horse, and that's nothing compared to what sometimes happens. People blaring their horn at us is bad- but doing it to a horse....the consequences can be much worse.
Drivers won't wait until it is safe to pass, just like with bikes.
We have the same problems, and we need to work together on this.