My daughter and I have been wondering this too. Actually, our buns are so active, we wonder if they sleep at all!
Mimzy tends to do that ‘legs kicked out from under him’ flop onto his side (terrifying when I first saw it, but now so adorable) and then it’s like his eyes roll back in his head because you can see the white conjunctiva on one side. Looks like a psycho-bunny! 0_o But sometimes he cuddles his little carrot plushie under his head, or if he’s too warm, likes to curl up next to his ceramic feeding bowl and cool his head with it. (usually there’s a freeze bottle for him to sleep or pounce upon…he likes to tear at it with his front paws)
Lately he’s been waking VERY early and throwing his litterbox around. Since I need to keep things quiet first thing so the hubby can sleep, I then have to remove that and pet him. For HOURS! >_< I like it best when he sleeps on the shelf in his cage and watches me sleep. I feel like I have a little bunny angel watching over me! ^^