As a young child, I was shocked and horrified to learn that the lotion my father regularly applied to his hands was, in fact, udder cream. As in it had the word "teat" on the label. Years later, I find out he was on to something.
Udderly Smooth Udder Cream is greaseless, scentless, and will leave your skin softer than you thought possible. The company does make a hand and body lotion aimed at bipeds, but I suspect that's just for the faint-at-heart.