nose has 9 distinct synonyms spread across 5 of its 14 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the organ of smell and entrance to the respiratory tract; the prominent part of the face of man or other mammals
“he has a cold in the nose”
a front that resembles a human nose (especially the front of an aircraft)
“the nose of the rocket heated up on reentry”
the front or forward projection of a tool or weapon
“he ducked under the nose of the gun”
a small distance
“my horse lost the race by a nose”
a symbol of inquisitiveness
“keep your nose out of it”
the sense of smell (especially in animals)
“the hound has a good nose”
a natural skill
“he has a nose for good deals”
a projecting spout from which a fluid is discharged
advance the forward part of with caution
“She nosed the car into the left lane”
Synonyms, antonyms and the broader and narrower relations for nose come from Princeton University’s WordNet. Full sources and licences.