Difficulty breathing through nose related to snoring?

Very likely: If you have difficulty breathing through your nose and snoring, it is very likely that the two are related, though there can be additional causes of the snoring and fixing the nasal breathing may not be the only thing that needs to be done. The best thing is to see an ENT for a full evaluation of snoring and to rule out obstructive sleep apnea, that can lead to tiredness and other health problems.

Yes: The airway ideally includes nasal breathing. When air goes through the nose and then behind the throat and into the lungs there is usually less obstruction. When your nose is blocked and you mouth breath there is more obstruction.