yes! we have Tennessee Walkers and they lay down all the time and for long periods of time w/out having a hard time getting up, they especially lay down at night and when they are about to foal. However I have seen one sit even as a trick.
Actually, being an equestrian and equine caretaker myself I can say to you that my horses do lie down every night for at least 5 hours, but some older horses just stand and cock one of their back legs. Horses do not sit naturally, but you can teach them.