It doesn't have to be an actual set time. Barns do set times because well, they're on a work day afterall. For a lot of barns, AM feed is the first thing done at the start of the workday and PM feed is the last thing of the day before going home. The start time of the workday is usually around AM feed time. The start time of the PM feed time is often early enough to allow people to get all the feeding done and be out the door at a reasonable time. The routine is nice because the horses learn to come in at particular times of the day. The only times I think set feeding times are kind of required is when food is limited (like when people do not feed free choice hay or when a horse is stalled or what-have-you) - because then the horse may be out of food and the checks ensure the animal is fed. If the horse is out on pasture or has free choice hay, then the time you feed grain won't matter.
(At least, this is the reasoning at the barns I've been at.)
* I'm often reading and posting from mobile and Siri loves to make a mockery of the English language.