The Bible says nothing about a horse. Read it.
It’s just artist’s depictions that have us thinking that Saul was riding a horse.
Acts 9:3-4
As he neared Damascus on his journey, suddenly a light from heaven flashed around him. 4 He fell to the ground and heard a voice say to him, “Saul, Saul, why do you persecute me?”
Since; like Elwood and Jake; Paul was on a Mission from GOD. It is assumed he'd be riding instead of WALKING the entire distance to Damascus.