It's possible that no one knows the answer to this question. We could never find one. But the question shows why science is exciting: there are always questions that have not been answered. Here's what we learned.
The skin covering a dog's nose may become wet from the dog's own breath. When a dog pants, it breathes in (mostly through the nose) and breathes out (mostly through the mouth.) But in quiet breathing, much of the breathed-out air flows through the nose. This air is warm and humid, and if the outside air is cooler, some of the moisture is likely to condense. That may keep the nose wet.
Also, dogs often lick their noses. We don't know if they do it often enough to keep their noses wet, but it's something you might watch for and think about when you see dogs.