It’s what you sniff
It’s what makes you snore after having your way with it
Its hairs cause you to sneeze if they get in your nose
It’s where you put your snout
If it has a yeast infection, the result looks like snot
Snort is the sound it makes when air gets trapped inside
When clean, it has a pleasent scent
When used properly it can really clean out your sinuses
The roots of “nose” are very ancient, going back to PIE.
Since “n” is a nasal sound, it’s no coincidence that a lot of sounds associated with the nose also have an ‘n’, since many (snort, sniff, sneeze–originally fneeze–, etc.) are imitative in origin. That is, a word that sorta sounds like the sound it describes.
“Scent” appears to be related to the word “sense,” which might have originally referred to “smelling” or “sniffing” as a hunting dog might do. So that might also be another “n” word related to the nose.
“Sinus” is coincidental. “Sinus” by itself has no nasal connotations, but commonly we refer to the “paranasal sinuses” as the “sinuses.” But “sinus” has the same root as “sine” as in the curve.
I don’t know, but there was a cartoon about this in a Ripley’s Believe it or Not book from the 1960s saying that there were ( insert number here) words associated with the nose that began with “sn…”. The cartoon may well have dated back to the 1950s or 1940s, and they were to polite to put “snot” in there, but they did list quite a few others. Not the whole list, of course. Things like:
snoot
snooty
snout
snort
sniff
sniffing
sniffle
etc.
I suspect that “n…s…” words (Nose, nasal, etc.) go back to a common Indo-European root, but the “sn…” stuff is from a different soource, probably onomatopeia (“Snort” and “sniff” sound kinda like those words).