The correct answer is - slow down, leave enough space, and accelerate slowly once passed.
When coming to a situation on a rural road where there's a person riding an animal, usually a horse, there's few steps that should be taken in order for an incident to be avoided.
First, you should slow down slowly from a bigger distance. Than make sure that there's enough space between the animal and the vehicle, approximately one car space in between while passing. Make as little noise as possible. And once the animal is passed, accelerate very slowly until you get further away from it.
