also horse-shoe, late 14c. (early 13c. as a proper name), from horse (n.) + shoe (n.). Horseshoes as another name for the game of quoits is attested by 1822.
HORSE-SHOES, the game of coits, or quoits--because sometimes actually played with horse-shoes. [John Trotter Brockett, "A Glossary of North Country Words," 1829]
The belief that finding a horseshoe by chance is lucky is attested from late 14c., and the practice of nailing one above a doorway to prevent a witch entering (or leaving) was common in London down to c. 1800. Of a type of bend in a river, 1770, American English. The horse-shoe crab of the east coast of the U.S. so called by 1809, for its shape; earlier simply horse-shoe (1775); also horse-hoof (1690s), horse-foot (1630s), which Bartlett (1848) identifies as "the common name."