In my young days, I used to ride and have seen this from both sides. So, here a few pointers for passing horses.
Communicate by perhaps given a cheerful “hello” when coming approaching. This can help the horse and rider be aware of your approaching. Horses can be spooked by things that suddenly appear without noise. Follow instructions given by the rider.
Slow down you move too fast (song spinning in my head, thanks to Simon and Garfunkel Feelin’Groovy). Move slowly and careful pass. Be prepared to stop.
Space should be given. All horses can spook, even the ‘Bombproof’ ones. Give as much space as you can.
No sudden movement or noise hard braking or changing gear can cause a horse to spoke
Be visible, make sure that both horse and rider can see you clearly
Be polite and hopefully we can all get along on the ride.
A useful leaflet with further information can be found on the British Cycling site.