What makes a mammal?
Among vertebrate animals, only mammals have hair. All mammals have at least some hair, even if not much more than eye lashes or whiskers.
Hair provides insulation from the cold and heat of the environment. Marine mammals that lack fur insulate their body heat from the cold water with a layer of body fat, or blubber.
Hair may also provide camouflage (visual protection) in addition to physical protection.
Individual hairs may also provide touching sensation, which is the function of whiskers (vibrissae).