1580s, from Dutch or Flemish snuffelen "to sniff about, pry," related to Dutch and Flemish snuffen "to sniff" (see snuff (v.2)). Related: Snuffled; snuffling.[snuffle etymology, snuffle origin, 英语词源]
1764, "sound made by snuffling," from snuffle (v.). Old English had snofl (n.) "phlegm, mucus." The snuffles "troublesome mucous discharge from the nostrils" is from 1770.