late 14c. (early 13c. as a proper name), from horse (n.) + shoe (n.). Horseshoes as another name for the game of quoits, attested by 1822.
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 therein was common in London down to c.1800. Of a type of bend in a river, 1770, American English. As a type of crab, from 1775.