If you love white dogs, you have many to choose from. First, you have to determine the size that you want. If you are not sure if you want a large dog or a small dog, below are two types that are pure white in each size. You can then decide and bring your puppy home with you. Coton de Tulear Coton de Tulear, also known as Coton, are small dogs that are pure white, which is where they get their name.