Horses have a 'stay apparatus' in their legs that they 'lock' when they go to sleep standing up. Sometimes you can hear a very soft click in an older horse when they unlock it.
Ours can choose to be out or in. Their stalls are their 'mane caves'. They generally lay down in their stalls, unless it's absolutely perfect outside - warm, sunny, a light breeze, and not a bug in sight. Then it looks like our pasture is full of dead horses...stretched out flat, LOL. My neighbor's horses are the same, further, he's got a mare and foal who will NOT stay outside, they sneak in and lie down in the stalls during the day, LOL. But they have an ulterior motive - they prefer to stay in the shade and nibble up the little stray bits of hay laying around.
Them laying down in their stalls doesn't necessarily mean colic. I look for changes in their chosen routine. Such as them lying down in places they don't routinely choose - and in unusual positions. A fine mist of sweat on the foreface is also a tip off, as is a distant, preoccupied look. They may look dull or depressed. Or - look back at their belly, try to pee and get only a few drips, etc.