I've noticed a lot of old men with big noses. do noses get bigger with age?

Yes: One way we subtely tell people's age is the ratio of ear or nose. Bones stop growing after puberty;cartilage does not.

Rhinophyma: You may be talking about a condition called rhinophyma. It may be associated with a skin condition called rosacea. It is indeed classically seen in older males. As these patients age, the nose may become bigger. Surgery is sometimes needed to help reshape the nose.