Having worked in shelters and in animal hospitals, I have seen many sick dogs come in with wet noses. Sometimes you can't tell at all when an animal is sick. Sometimes they're happy, wagging tails, bright eyes and all. Sometimes the ones that look sick are fine. The best way to tell, at least in my opinion, is to see if the dog's behavior is different than normal. Sluggish, not eating or drinking, sleeping a lot, no interest in playing. That kind of thing.