What is the proper etiquette for overtaking a horse? What are the general rules when encountering a mounted rider (on a horse) on a trail? I understand if we are approaching each other I would dismount, move to the side of the trail and allow them to pass. However if we are traveling in the same direction and I am overtaking them (say going down hill) how would you alert the rider and not startle the horse? I have not yet come upon a rider on my regular trails but I have noticed an increase in road "apples", so I know it is inevitable.I have heard that dismounting is important as the horse may not recognize you as a person due to the unusal movement(from the horses perspective).
Passing a horse, mounted or otherwise, should be done so:


very slowly
as quiet as possible.  If you have a loud freehub, pedal slowly -- do your best not to coast.
with as much space &amp; consideration as possible
no sudden movements 
limit the number of cyclists going past


It all depends on the horses' temperament.  Some are OK, some like cars but not bicycles...
Generally, horses with kids/teenagers riding them on the road will be pretty laid back.  The horses that are being led by someone are much more suspect.  

Competent equestrian owners/staff know that any horse [that will be taken or ridden on roads] needs to be exposed very carefully (for the safety of the horse, the rider, and the general public).  They have to accept that the horse may never be comfortable in that setting.  But anything could spook the most experienced horse - you never know 100%.

If possible, send a single person ahead to talk to who has control of the horse while watching how the horse reacts.