Dogs' noses stay wet for several reasons, with the main one being that they continuously lick their noses. The continual wetness of the nose also helps the dog to detect smells.
The moisture on the nose makes even the slightest odors easier to smell. This is one of the reasons a dog's sense of smell is much more acute than that of a human's. It is also believed that a wet nose helps the dog stay cool. With so much fur, it is hard for dogs to cool down, so they dissipate heat through their mouths and nose s. As this happens, the heat evaporates, causing their mouths and noses to stay damp.