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]

WordNet (r) 3.0 (2006):

snuffling
    adj 1: liable to sniffle [syn: sniffly, snuffling,
           snuffly]