A person's nose or snout; also used informally to describe a snobbish or stuck-up person.
Probably a variant or blend of 'snout' and 'nose,' with roots in Scandinavian languages (compare Old Norse 'snut'). The word gained popularity in 20th-century informal English. The snobbish sense developed metaphorically from the image of looking down your nose at someone.
Calling someone a 'snoot' for being snobbish is literally perfect: if you're being a snob, you're metaphorically 'looking down your nose' at others. The word sounds dismissive and cute at the same time, which is why it's perfect for gently mocking pretentious people!
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