We occasionally get horse riders about in my town, on the cycletracks. I encounter the “waste” much more than the horses. It hangs around for ages and never seems a priority for the council. But I agree, it could be much worse!
When I do encounter horses however, I must say they are a danger. Most recently, a very large white horse, with only a piece of rope to lead it! I don’t think it had ever seen a cyclist before. The owner did look a bit like a Gypsy (if I’m still allowed to call them that).
Another time was when I was lining up to overtake a horse rider, giving plenty of room. I checked behind me, started to accelerate and without warning, the horse began to turn right. No signals, backwards glances or road positioning, almost as if the horse knew where the rider wanted it to go. Luckily I was able to abort the overtake. I wasn’t going to pass very quickly anyway.