As mentioned, doggie noses should ordinarily be moist to assist with cooling down. If the nose becomes too dry, the skin can crack and become damaged.
When you get nervous, you probably have some sort of indicator. Maybe your hands start sweating, or your heart beats noticeably faster. In dogs, stress can manifest as excessive nose-licking.
Involuntary Nervous Tick
Sometimes the general stress action of licking a nose goes into slightly deeper territory – that of a nervous tick.
This could be seasonal or have to do with the environment. Like when humans suffer allergies, they tend to wipe away the causes of the irritation.
A dog may suffer from dehydration for several reasons, like not having access to enough clean water. It may simply also be too hot, leading to an excessive loss of moisture.