Synonyms for Snuffle (same or very similar meaning)
WordNet sense 1 (sniff or smell inquiringly):
snuffWordNet sense 2 (the act of breathing heavily through the nose (as when the nose is congested)):
sniffle, snivelWordNet sense 3 (cry or whine with snuffling):
blubber, blubFrom the ODE community, based on WordNetadd/edit