A dry nose in a puppy (or an adult dog) is generally nothing to worry about. Several factors can account for a warm, dry nose such as sitting in the summer heat, air conditioning, central heating, dehydration or spending a lot of time in a room with poor circulation. A puppy's nose generally can vary between dry and wet throughout the day. A dry nose may also merely indicate that your puppy is not in an active sweating phase. Dogs have sweat glands in their nose and footpads and both will feel cool and wet when the dog is sweating. Panting is the other part of a dogs cooling system to help dissipate internal heat.
Symptoms of a problem
If you notice other abnormal signs such as yellow, green or black nasal discharge, sneezing, coughing, vomiting, diarrhea or sores and cracked skin on the nose then more serious conditions may be present and need to be evaluated.