Terminology
The term "muzzle", used as a noun, can be ambiguous. It can refer both to the protruding part of the face itself, and also to a type of apparatus placed over the protruding part to prevent the animal from biting or eating, often used before and after horse races or to control dogs. See animal muzzle for the latter meaning.
The wet, naked surface around the nostrils of the nose is known as the rhinarium (colloquially this is the "cold wet nose" of some animals). The rhinarium is often associated with a stronger sense of olfaction.
Read more about this topic: Snout