A dog's nose is supposed to be wet if they are healthy, just not runny. They are susceptible to allergies just as we are, so if it's nose is runny and not just wet, it may be allergic to something. If it is dry, it usually shows that they are sick for some reason. If they are sick, watch to see if they eat grass when outside, that usually is a definite sign of some sickness, but allow them to eat the grass or weeds they chose because nature has installed in them the reasoning to know what grasses to eat for different kind of sicknesses.
Dry if its not helthey but wet if its helther
I don't think it matters but they have a wet nose so they can smell better