The skin on the palms of our hands and soles of our feet is hairless - and it is this lack of hair that causes our hands and feet to go wrinkly after a soak in the bathtub. In other areas of the body, sebaceous glands which are attached to hair shafts produce oils that help to waterproof the skin.
Without this natural waterproofing, the palms and soles are more prone to absorb water.