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"lustful, sexually aroused," definitely in use 1889, perhaps attested as early as 1863; from late 18c. slang expression to have the horn, suggestive of male sexual excitement (but eventually applied to women as well); see horn (n.).
horny horn·y (hôr'nē)
adj. horn·i·er, horn·i·est
Made of horn or a similar substance.
Tough and calloused, as of skin.
Sexually excited and desirous; keenly amorous; lustful; hot •Of recent years applied to women as well as men, despite being derived fr horn, ''erect penis'': his horny teen-age daughter/ At first it eased my head and made me less horny/ a few scenes between a horny housewife and a guy in a Lone Ranger mask (1889+)