Apologies. I removed my posting because I made an error after the part that T42 quoted, and I wanted to rethink.
I would understand the meaning to be two between them.
The singular implies collective possession of one item, and the plural is most likely to mean one each; the plural could mean that the crowd shares more than one, but less than one each, but the context should make this clear.
If ambiguity is a real concern, you can introduce "each" to resolve it: Men, each with a big nose and a small nose. As Cudzoziemiec suggests, given that the possession of anything other than one nose per person is inherently improbable, the need to resolve ambiguity would always apply to noses.
If you wanted to express the fact that many men shared fewer, but more than one, noses, you would have to write this more explicitly. I doubt that you will find yourself doing that too frequently.