"Unlike humans, who cool themselves largely by sweating, dogs cool themselves through their respiratory tract through panting, pushing warm air out and bringing cool air in," Dr. Sonja Olson, a senior clinician in emergency medicine for BluePearl Veterinary Partners, told The Dodo. "Cooling occurs as moisture evaporates from the tongue and nose, which both have a lot of blood vessels close to the surface."
So, when your dog is running around a lot or the weather outside is incredibly hot, his nose is likely to be cold, as his body is trying to keep him from overheating.
On a not-so-hot day though, or on days where your dog isn't as active, his nose might not feel as cold, and that's perfectly normal. The coldness of a dog's nose relates directly to his cooling system, and on days when he doesn't need to keep as cool, his nose just won't be as cold.