The most common cereal grains that are included in horse feeds are oats, corn, and barley. These grains are included in the feed to provide for energy but not all of them are equal. Two main factors that affect the safety and performance of these grains in horse feeds are the starch found in the grains and the grain processing. The starch found in cereal grains is what supplies energy to the horse. However, an excess of starch can lead to obesity, over excitability, and metabolic problems in horses. Oats tend to have the lowest starch level and corn typically has the highest. Because of this, corn is much more energy dense and should be fed in lower amounts. It is important to keep in mind that corn starch can tend to be less digestible unless it has been processed in some way (cracked, flaked, etc.).
As long as you recognize that the starch content of the corn is going to be higher and that less is needed, feeding processed corn in the correct amount is alright to feed to horses. It is when corn is overfed that digestive upsets do occur and cases of colic or acidosis does happen. I would advise that if your horse is not working heavily or in need of any supplemental calories (energy), simply feeding forage for the time being should be sufficient.