early 13c., "trunk or projecting nose of an animal," from Middle Low German and Middle Dutch snute "snout," from Proto-Germanic *snut- (source also of German Schnauze, Norwegian snut, Danish snude "snout"), which Watkins traces to a hypothetical Germanic root *snu- forming words having to do with the nose, imitative of a sudden drawing of breath (compare Old English gesnot "nasal mucus;" German schnauben "pant, puff, snort" (Austrian dialect), schnaufen "breathe heavily, pant," Schnupfen "cold in the head;" Old Norse snaldr "snout" (of a serpent), snuthra "to sniff, snuffle"). Of other animals and (contemptuously) of humans from c. 1300.
"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.