In the book Empire of the Summer Moon the authors claim that only the Comanches were very adept at this.
Most tribes did not fight on horseback and the comanches were very successful at displacing other tribes in such a large area because of their skills on horseback. In fact until the six shooter and repeating rifles americans and texans could not win a fight because comanches could fire more arrows before a soldier could reload a gun.
It is a very interesting book. Shalom