I realy dont know if they sleep or if they just rest. I walked up on some bedded does durring season and just watched them for about an hour through my binoculars. There was three of them and there was always atleast one keeping look out. They didnt seem to be sound asleep, but they would close there eyes for about a minute at a time before opening them again and becomeing alert. Another time I walked up on a small buck and he was faceing the other way. His head was up with his eyes closed and his ears pointed straight back for the twenty of thirty minutes I was watching him, and when I tried to sneak away without disturbing him he spooked and took off.