Every situation is different. Horses and riders have different levels of experience as cyclists do.

I have ridden horses with bikes going by and been on a bike in the presence of horses. Most horses under saddle may spook when they catch sight of you but most are not going to continue to misbehave if they are allowed to get a good look at you. I would never expect a cyclist to get off and walk even if my horse continued to misbehave. The best thing is to ask the rider and then for everyone to just continue on their way.