The horse knows you are there long before you are in earshot of the rider - the side eye position gives them 350Degrees monocular vision, the only blind spot is directly behind. A slight sideways head movement while you are some long way back is probably the horse having a good look"
Epsom downs and environs is our prime cycling territory and/we normally find that a widish approach and a single "ding" from a long way back is enough to let the rider know of an approaching bike, but as one rider said recently as i approached on quite a narrow track, and asked "ok to come through?" ...."Don't worry, she told me you were there ages ago"
Pass wide and slow and observe is the horses demeanour changes as it senses your presence ie skittishness.
Old hack rides are generally no problem, highly strung thoroughbreds on or around the racecourse are a different beast altogether, and for the safety of all a very cautious approach is well advised, even when approaching in opposite directions. I generally stop till they pass and even then the rider sometimes struggles to control a young inexperienced horse who has never seen a bike before and finds bright clothing intimidating. Travelling in the same direction the opposite side of the road is best, or if i know where they are turning, i simply wait till they move off the road/track and always get a wave of appreciation even when have not spoken to the rider or them having looked back.