Corn is the worst feed of all for a horse because it's so high in starch (sugar) and can make them colic - which is comparable to the worst upset stomach you've ever had times 10. Colic can and often does lead to death because horses cannot regurgitate or throw up like humans can. With that said, when corn IS fed, it's usually not on the cob, but rather cracked, rolled, or steam flaked or pressed.
Yes, there are still people who insist corn is okay to feed to horses. Those folks will normally throw the entire corn cob in. If a horse has, say 10 corn cobs to choose from, they will eat the corn part first, then go to the next ear of corn and eat that corn. The cobs are left til last. Whether or not a horse eats all of it depends on many things - the horse's metabolic make-up (some horses will eat anything anytime it's handed to them...those horses are called 'easy keepers,' but that's not always a good thing. They over-indulge and gain weight, which leads to feet problems (founder) and fat deposits underneath their skin, plus they get lazy if not exercised regularly.) Those easy keepers will plow through the cobs without hesitation.
Another type of horse, referred to as a hard keeper, wouldn't touch a cob, and most likely won't eat all the corn off the cob. They need a special diet to keep weight on them, but it's usually not corn.
Then there's the regular horse who is unpredictable and normally more reserved. They may leave the cob to dry out before eating, or may not eat it at all. Think of the cob as the cereal we humans call Shredded Wheat - without the frosting on top.
I don't think this answered your question, but there are too many variables to say it's normal for a horse to eat the corn from the cob, then eat the cob itself. Horses are finicky creatures and what they do today may not be what they do tomorrow.
Did I thoroughly confuse you? LOL!