(Quest is only available in 3.9.4 and later)
Barding begins with the newly hired blacksmith of your Hideout, Harold, locating some unique horse armor in the ruins, but no existing horse can equip the armor. You need to go to the the old capital of Pendor (the city of Sarleon) to uncover more information on the old horses that used this.
Talk to the horse merchant of Sarleon, Squire Cathan, about old horse breeds. He mentions that he has three of the old Pendor Royal Steeds in stock, and is ecstatic about the prospect of seeing one of them in the original armor. He'll sell you one of his steeds for a Medium Pouch of Diamonds.
Once you have the horse quest item, bring it back to Harold in your Hideout. After two weeks, he'll have the unique Pendor Royal Steed fully armored and ready for you. You'll also earn a level-based amount of experience.