No, a wet, cool nose can indicate good health. However, warm and dry nose does not mean there is a serious problem. The best things to watch (in my opinion, my opinion and I am not a vet, but I do own three beagles) is to notice if there any change in their eating habits, are they spending more time sleeping than usual. Are they scooting, check their ears and coats for bites, ticks or unusual bumps, etc and pay attention to the dog's attitude--is he pulling away from family members, is he barking more for no apparent reason. If you see any combination of these conditions, and they continue for more than a day or two, you should call your vet.