Though a cat's nose does indicate its general well being, a dry nose does not necessarily point to any kind of serious illness. Knowing what is normal for any individual pet is key.
Cat Nose Health
A cat's nose can be dry or moist at any given moment without the animal being ill. The cat has many sweat glads in the nose, and these play into the dampness and temperature of the nose. As the glands in the nose become more or less active, the nose can be wetter or drier and this can mean virtually nothing as far as the cat's overall health.
Dry Nose with Other Symptoms
If a cat simply has a dry nose, this is usually not cause for worry. However, if the nose feels both dry and warm to the touch and the ears also feel warm to the touch, the cat may have a fever. If the cat has dry gums, this can be a sign of dehydration, which may signal a larger illness. You should generally aim to be aware of the pet's normal state of being, so you will notice such symptoms.
If the cat's nose seems overly wet with a small amount of discharge, this is usually OK. However, if the nose seems extremely wet and there is a large amount of discharge, this can mean the animal has a cold of some kind and a vet visit is probably in order. A normal amount of discharge is easy to discern as it usually forms as a drop on the end of the cat's nose.
A dry nose that is sensitive to the touch or red can signal the cat is allergic to something. Most likely, the animal is allergic to its bowl. If the bowl is plastic, consider changing to a metal or ceramic bowl. A veterinarian can determine if the nose sensitivity and dryness is the result of an allergy.
Cats are prone to allergies, colds and other nasal infections. An animal can sneeze once or twice and this is normal, but if the animal begins to sneeze chronically, consider a vet visit.