The Collaborative International Dictionary of English v.0.48:

Snuffle \Snuf"fle\, v. i. [imp. & p. p. Snuffled; p. pr. & vb.
   n. Snuffling.] [Freq. of snuff, v.i.; akin to LG. snuffeln,
   G. schn["u]ffeln, D. snuffeln, Dan. sn["o]vle. Cf.
   Sniffle.]
   To speak through the nose; to breathe through the nose when
   it is obstructed, so as to make a broken sound.
   [1913 Webster]

         One clad in purple
         Eats, and recites some lamentable rhyme . . .
         Snuffling at nose, and croaking in his throat.
                                                  --Dryden.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Snuffle \Snuf"fle\, n.
   1. The act of snuffing; a sound made by the air passing
      through the nose when obstructed.
      [1913 Webster]

            This dread sovereign, Breath, in its passage, gave a
            snort or snuffle.                     --Coleridge.
      [1913 Webster]

   2. An affected nasal twang; hence, cant; hypocrisy.
      [1913 Webster]

   3. pl. Obstruction of the nose by mucus; nasal catarrh of
      infants or children. [Colloq.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

snuffle
    n 1: the act of breathing heavily through the nose (as when the
         nose is congested) [syn: snuffle, sniffle, snivel]
    v 1: sniff or smell inquiringly [syn: snuff, snuffle]
    2: snuff up mucus through the nose [syn: snuffle, snivel]
    3: cry or whine with snuffling; "Stop snivelling--you got
       yourself into this mess!" [syn: snivel, sniffle,
       blubber, blub, snuffle]