Every horse is different and every situation is different.

One of my horses would not care if you ran into her with your bicycle. Another of my horses would flip out if he saw a bicycle (and has done that with me more than once because of a bicycle).

Horses are very large powerful animals. Some of them lose all sense of self preservation when they are scared and could injure themselves, their rider, or the cyclist. It is always best to assume that the horse is going to spook and approach with caution letting the rider know that you are coming.