Horse riding was much less popular than you think. What was much more popular was horse-powered carriages, which are much more convenient than riding, and also less dangerous. Horse riding was pretty much a hobby, a hobby of the rich at that. Try reading some books from the era. For example, in Steinbeck’s “East of Eden” there is a quite funny moment when Hamilton sons were going for dances, when two older brothers already took family buggies, the younger didn’t choose to ride on a horse, but did something quite different, which made his mother very unhappy.