"proud, arrogant," 1918, noted that year as college slang, from snoot (n.) + -y (2). Probably with suggestions of snouty (1858); the notion being of "looking down one's nose." Related: Snootily; snootiness.
The nose; snout; schnozz: Pokin' him one in the snoot (1861+)
To behave haughtily toward; disdain: people who snoot goat milk (1928+)