The Collaborative International Dictionary of English v.0.48:

Sniffle \Snif"fle\, v. i. [Freq. of sniff. See Snivel.]
   To snuffle, as one does with a catarrh. [Prov. Eng.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

sniffle
    n 1: the act of breathing heavily through the nose (as when the
         nose is congested) [syn: snuffle, sniffle, snivel]
    v 1: cry or whine with snuffling; "Stop snivelling--you got
         yourself into this mess!" [syn: snivel, sniffle,
         blubber, blub, snuffle]
    2: inhale audibly through the nose; "the sick student was
       sniffling in the back row" [syn: sniff, sniffle]