Cows lie down (so do horses, another animal thought not to lie down unless ill, though not for very long). They like to take a load off now and then, just as much as anyone and lay down a lot through the day.
Fun fact: Cows like water beds. Dairy farms in recent years have been starting to use water beds/pads in the barn for cows to stand and lay down on. They love it. It helps them rest and relax, and increases milk production.