My google searching has turned up a lot of odd-looking shoes for humans, a couple of vague references to goatshoes and a culture that wrapped their goats' hooves in something to protect them, and lots and lots of instructions on how to trim a goat's hoof, but nothing really solid.
Terms searched: "shoe a goat", "shod goat", "shoes for goats", "goatshoes"/"goat shoes", "can you put shoes on a goat", "can you shoe a goat", "protect a goat's hoof", "shoes on cloven hoof"/"shoes on cloven hooves", "cloven hooves shoes", etc etc etc
EDIT: Wow, I didn't expect so much of a response! Thank you everyone for your input, I think I can work this out now! (And for those who asked, I didn't want to use the "traditional" magical-bridle method for various story reasons, so that's why I was going with this.)