You'll see a horse described at this in Medieval literature and sometimes in fantasy.
Caparisons are cloth covers that were put over the armor, usually during tournaments.
This illustration from a book currently in the French National Library, attributed to an artist named Bathelemey d'Eyck, shows sword-wielding knights fighting in a tourney. The caparisons on the horses match the tunics worn by the knights. I suspect that the covers on the reins were a little more than just decorative - they would have made it harder to either grab or cut the reins during a fight.