The story
To have something up one's ass (= stowed there) is (in cynical jocular formulation) to have it on hand and available despite the unlikelihood of being so equipped. (You're going to patch that tire right now, out here? What, do you have a patch kit up your ass?) A horseshoe is a traditional good luck charm in folklore. Thus, to have a horseshoe up one's ass is to have an unlikely amount of luck and to carry it around continuously in a way that seems unexpected.
Etymology from Wiktionary, CC BY-SA 4.0.