I was told this too and believed it for many years until I telephoned the vet once and spoke to the nurse as my dog was under the weather, but I mentioned that her nose was cold and wet. She then told me that it didn't mean anything and it was an old wifes' tale!
A: We've sure felt them cold and wet pressed against us but dogs' noses are not always cold, even when they're well. A dog's nose changes through the day: wet and cool one moment and warmer and drier the next. The nose wetness (or lack thereof) also changes with the humidity. The nose norm varies from dog to dog.
Stiv, DogNose Heaven
Wet and cold (for now).
A dog's nose, though, tends to be cool and moist just as the inside of a human's nose.
"A dog has special glands inside his nose that secrete a watery fluid to keep the inside of the nose moist and to help cool the dog through evaporation," says Holly R. Frisby, veterinarian at Drs. Foster & Smith, Inc. This moisture can extend to the outside of the nose, making it shiny, wet, and cold.