Nasal temperature and moisture does not tell us anything about the health of a dog.  For example if your dog has been active or sitting in the sun the nose will feel warm.  Nasal discharge or changes to the cobblestone appearance is not normal.

I always heard a healthy dogs nose should be wet.

Petsareagift.com

Yep a cold and wet nose. Sometimes warm, though.

Wet cold nose when active, but if they just woke when sleeping it is sometimes dry from breathing through it and without licking it.

Wet tempature dont matter

I have always heard cold and wet, too. My dogs' noses always seem cool but not really wet, maybe just a little moist. I know dry or scaly is not good, but neither is dripping or running.

A cold, wet nose is a healthy pup :)