Actually, current research supports what Kaykay said-that it is not a good idea for horses to do significant work on an empty stomach, for the reasons she cited.
If you consider how a horse's digestive system is set up, this makes sense to me. Now, shortly after a FULL feed, or a signficant grain/concentrate feed? No, a horse should NOT be asked to work hard....but there is published evidence now that if it's been HOURS since a horse had anything to eat, it would be best to give a light (hay) feed an hour or so ahead of the time you'll be working the horse, so that there IS something for the stomach acid to 'work on' ( besides the inner lining of the stomach )while the horse is worked. The horse will most likely feel better, have a better attitude and ability to focus, too.
When I was showing, I NEVER took a food (or water--even worse!)-deprived horse into the ring to show, as I have heard and seen some do. It is unkind to the horse, and may well be downright dangerous to their intestinal, and therefore, their overall, health. The harder the workout, the more important proper consideration to this, and to a proper cooldown afterwards, becomes.
Margo