Etymology

horny (adj.)

late 14c., "made of horn," from horn (n.) + -y (2). From 1690s as "callous, resembling horn." The colloquial meaning "lustful, sexually aroused," was in use certainly by 1889, perhaps as early as 1863; it probably derives from the late 18c. slang expression to have the horn, suggestive of male sexual excitement (but eventually applied to women as well); see horn (n.). As a noun it once also was a popular name for a domestic cow. For an adjective in the original sense of the word, hornish (1630s) and horn-like (1570s) are available.

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Definitions of horny

horny (adj.)
feeling great sexual desire;
feeling horny
Synonyms: aroused / randy / ruttish / steamy / turned on
horny (adj.)
having horns or hornlike projections;
horny coral
horny (or horned) frog
horny (adj.)
made of horn (or of a substance resembling horn);
Synonyms: corneous / hornlike
From wordnet.princeton.edu