You’re quite correct, of course, about there being no scriptural predicate for a horse. The last time I posted this story a commenter made the same point and added that the Roman occupiers very probably would have barred the Jews from owning or riding horses.
So, if Paul was in fact riding, a donkey would have been his conveyance. To an artist, though, a horse is sexier.
He would not have been riding a 17th century “high horse” in any event! Roman horses (assuming because he was a Roman Citizen he was authorized to have one - Acts 22:27) were lighter in weight and finer in the head (more like Arabians).