Yes most of the time. Like horses they prefer that, but sometimes they nap while laying down.
It depends on what you mean by "sleep." Just as you can sit in a chair and nap with your head on your folded arms in front of you on a desk or table, a horse can nap standing up. However, just as most of us cannot get a full night's sleep on folded arms at a desk or table, most horses cannot get a full night's sleep standing up.
If you get up in the middle of the night and sneak in a barn where horses were stalled, safely and securely hours before, you would find them all lying down. Of course, you have to be quiet, as horses are very weary and have very good hearing. If they hear you come in and are alarmed, they will stand before you get to them.
Horses spend the night (or a good portion of it) lying down and Zebra's are no different.
If you get up in the middle of the night and sneak in a barn where horses were stalled, safely and securely hours before, you would find them all lying down. Of course, you have to be quiet, as horses are very weary and have very good hearing. If they hear you come in and are alarmed, they will stand before you get to them.
Horses spend the night (or a good portion of it) lying down and Zebra's are no different.