As a horse rider, I tend to find it's mopeds and not bicycles that are most likely to send my horse careering sideways across the road. That said, horses can be unpredictable, and even horses that are pretty bombproof* can sometimes freak out about things they're usually fine with**. Shouting or bells may well upset some riders, so I just go for slowing right down, calling out 'passing on your right' and pass wide and slow, in the other lane if you can.
As a horse rider, I tend to find it's mopeds and not bicycles that are most likely to send my horse careering sideways across the road. That said, horses can be unpredictable, and even horses that are pretty bombproof* can sometimes freak out about things they're usually fine with**. Shouting or bells may well upset some riders, so I just go for slowing right down, calling out 'passing on your right' and pass wide and slow, in the other lane if you can.
*not literally
**usually plastic bags