The Mare Goddess makes her appearance during only one chapter of the book, and we never figure out who is in the Mare Goddess costume, though she makes quite an impact. Besides being a woman with a real decapitated horse's head on her own (um, ew), making her look like a classic Zelda character, she brings with her a wealth of information about the lore of the island.
First, she's part of a ritual in which, over the course of one night, she will drop a single shell. Whoever grabs the shell can make a wish. It happened to Sean when he was a kid, although his vague wish may or may not have come true. This gives the Scorpio festivities a bit of a Mardi Gras feel, albeit with less flashing.
Also, her costume is inspired by Epona "the mother of all horses" (32.42), not this other Legend of Zelda character. Epona is a pagan goddess of horses, rooted in Celtic lore, so this serves to give the legend of the capaill more validity.
Finally, it's a little strange that the deity behind all this is a goddess, yet the men of the island can't bear to let an actual woman, Puck, participate in the races. What gives?