The rule for French and English heraldry was that if the device were an animal (e.g. a lion rampant) it would face forward (to the right side of the shield, from the bearer's point of view). There is a device where it faces the other way, but that device is referred to as "coward" (so the blazon would be described as: a lion rampant coward). So on a horse barding, the device faces towards the front of the horse on both sides, and so it would be reversed from the shield on one side. However, this rule was not followed in Spanish heraldry, where the device was duplicated on both sides of the barding, irrespective of which way that had the animal facing.