Old Wives' Tale: Canine Nose Temperature

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It’s a commonly held belief that a wet, cold nose indicates a healthy dog and a dry, hot nose indicates a sick dog. This is a myth! Here’s why: the temperature of dog’s nose can fluctuate hour by hour and day by day, depending on they’re environment or behavior recently. A very sick or critically injured dog could have a cold nose; conversely, a healthy dog could have a warm nose.
Moisture also does not necessarily tell us anything about health. While, yes, a very dehydrated dog might have a dry nose, a wet nose could indicate a nasal disease.
What can a dog’s nose tell us about his health? Like skin, an external organ which tends to reflect internal health, keeping an eye on your dog’s nose can be a useful indicator of some conditions. Texture, sores that don’t heal, and flaking are correlated with underlying health problems such as nasal hyperkeratosis. Abnormal discharge can also be a sign of a health problem.
Many times, though, a health problem would have to progress significantly to manifest in the appearance of a dog’s nose. Better to keep an eye on behavior changes, lack of appetite, and other symptoms that could indicate a problem much earlier.
 
Sources:
http://www.animalwellnessmagazine.com/articles/what-her-nose-can-tell-you/
http://pets.webmd.com/features/dogs-hot-nose