I've been to zoos. I've seen animals asleep. They don't sleep with their heads against windows. Also, you seem to have missed the "and fits the other clues". Because, news flash, a horse ain't it.
You are going to be mightily offended, then by this image showing a fish with curved lines instead of eyes to indicate sleep. Turns out, fish don't have eyelids. so better rush over there and tell them that they are doing comic shorthand wrong, and that you insist that they must remain anatomically correct, rather than use the standard shorthand to indicate sleep by having curved lines instead of eyes.
Because no matter how much you attempt to mischaracterise my argument, "those aint' his eyes, that's just emoting shorthand to communicate he is asleep" is not some outlandish idea. It is extremely common way of indicating sleep even in creatures who do not in fact close their eyes to sleep.
GW