mid-14c., "to check, reprove, rebuke," from Old Norse snubba "to curse, chide, snub, scold, reprove." The ground sense is perhaps "to cut off," and the word probably is related to snip. Compare Swedish snobba "lop off, snuff (a candle)," Old Norse snubbotr "snubbed, nipped, with the tip cut off." Meaning "treat coldly" appeared early 18c. Related: Snubbed; snubbing.
"short and turned up," 1725, in snub-nosed, from snub (v.). The connecting notion is of being "cut short."