We can see fur loss on a cat’s nose for numerous reasons, including skin cancer. However, additional reasons may include infection secondary to allergies, parasites, fungal infections, and even self-trauma. Seek veterinary care if you notice your cat’s losing fur anywhere on the body, as it could indicate an underlying illness.We can see fur loss on a cat’s nose for numerous reasons, including skin cancer. However, additional reasons may include infection secondary to allergies, parasites, fungal infections, and even self-trauma. Seek veterinary care if you notice your cat’s losing fur anywhere on the body, as it could indicate an underlying illness.