Douglas Harper's Etymology Dictionary
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). Compare French monter sur ses grands chevaux; "The simile is common to most languages" [Farmer].
Wiktionary
n. (context idiomatic English) An appearance or sense of smug superiority.
WordNet
n. an attitude of arrogant superiority; "get off your high horse and admit you are wrong"
Wikipedia
"High Horse" is a song written by Jimmy Ibbotson, and recorded by American country music group Nitty Gritty Dirt Band. It was released in January 1985 as the third single from the album Plain Dirt Fashion. The song reached number 2 on the Billboard Hot Country Singles & Tracks chart.
Usage examples of "high horse".
When die Martian understood that he was about to be forced to remain in a travel tank for thirty days he came down off his high horse and agreed to tell the truth as adequately as was possible.
Of course you can herd us all, with your steel shirt and your high horse and your sword at your hip!