Of course it isn't made of rubber. Rubber is from the rubber tree. A dog's nose is part of the epidermis or "skin" which is a living part of the body. Although the nose is pigmented and appears to be tough, thick region of integument it is actually composed of only three layers rather than the five layers found on other parts of the body. The outermost layer of cells on the nose is called the straum corneum (horny layer). The grooves within the epidermal surface give it its textured appearance. This texture is unique to every animal, much like fingerprints are in humans.