Most dogs have black noses, not all. The noses of Vizslas and Weimaraners, for example, are closer to their coat colours. And it’s not unusual for puppies to start out with pink noses that darken as they mature.
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In all likelihood, dogs have developed black noses as a protection against sunburn. While the rest of the animal’s body is protected by fur, the noses are exposed to the sun’s rays. Pink-nosed dogs and breeds that are hairless or have very thin hair on their ears need to be protected with sunscreen when they go outdoors, or they risk the same sort of cancers and burns that humans do.
The canine nose — or nasal planum — is normally cool and moist, but not always wet. It has no sweat glands. The mucus lining causes the moisture. The evaporation of moisture from the nose helps to cool the dog. This moisture also makes the dog more sensitive to odours. Generally a happy dog continually licks his nose. When the dog isn’t feeling well, he tends not to lick his nose. And this makes the nose dry. But this is not a direct correlation. The brachycephalic breeds (bulldogs, Bostons, pugs, etc.) have noses set so high on their muzzles that they can’t reach them with their tongues and thus the noses tend to become cracked and dry on the top.
Sources: The Telegraph (Kolkata, India)