A cold, wet nose is just one sign of wellness in cats and dogs and should not be considered in isolation as an indication of overall health. On occasion you will find a healthy pet with a warm dry nose. Perhaps they don't lick their nose as often, or secrete as much mucous. On the other hand a sick pet can have a cold, wet nose.
Dog's noses secrete a thin layer of mucous that helps to absorb scent chemicals. When they lick their noses, the dissolved scents are presented to the scent and taste receptors (olfactory glands) on the roof of their mouths. A cold wet nose is just one of the reasons why dogs have an amazing ability to detect scents.
Moist noses are also one of the ways that dogs can regulate their body temperature and cool down. Unlike humans, dogs don't have sweat glands. They secrete sweat from the pads of their feet and their noses.
When to see the vet
If your pet has a dry nose and is showing signs of illness or pain (check the links below for other signs you can look out for), they should see a veterinarian. Similarly, unwell pets with cold, wet noses should also have a veterinary check-up. If you notice any unusual nasal discharge you should visit the vet as it could be a sign of a medical condition. Normal nasal secretion should be thin and clear, whereas thick mucous or crustiness around the nostrils could indicate signs of an upper respiratory infection.