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originally (late 14c.) "fine, tall horse; war horse, charger" (high steed is from c.1300), also, like high hall, "status symbol;" figurative sense of "airs, easily wounded dignity" in mount (one's) high horse "affect airs of superiority" is from 1782 (Addison has to ride the great horse in the same sense, 1716). Cf. French monter sur ses grands chevaux; "The simile is common to most languages" [Farmer].
To be on one's “high horse” is to be disdainful or conceited: “Sally got tired of Peter's snobbery and finally told him to get off his high horse.”