It is normal for cats to have wet noses. In order to improve the sensitivity of their sense of smell, cats often lick their noses to wet them. This operation helps capture odor molecules in the air, so the nose is dry only when the cat is sleeping. If If your cat doesn't sleep but has a dry nose, it's probably sick.

Tip:

Cats, like dogs, rely on their sense of smell to understand the world, so they rely more on their noses.