Cats have wet noses when they are hydrated. However, a cat with a dry nose does not necessarily indicate dehydration. The time to call the vet is when the cat goes from having a wet nose to a dry nose.
It is also possible for a cat's nose to be too wet. If a cat is suffering from an upper respiratory infection, a runny, dripping nose is a noticeable symptom. The most common cause of an upper respiratory infection in a cat is feline herpes. A cat with feline herpes experiences outbreaks from time to time and develops a runny nose.