Have you ever licked your finger to feel which direction the wind is blowing? If so, then you know the main reason why wet mammal noses, called rhinariums, are wet. It allows a mammal to easily detect changes in temperature on its nose due to evaporation and therefore know which direction a smell came from. Meaning, if the right side of your nose feels cold at the same time you smell something yummy and delicious, then maybe you should go to the right since that seems to be where the smell is coming from.
Evolution has made sure the nose stays wet by capillary action between the ridges of the nose and by the secretion of special moisturizers.
Why do many rhinariums have a split up the side? To expel air out. The large, forward facing channel is for intake, and the sides can be used to expel air. When a nose is down on an odorant, expelling air through the sides avoids disturbing where the smell came from. It also may avoid smelling an odor on an exhalation, which tells the individual less specific and often outdated information.