The horses hoof is made from the same thing as our finger nails, and our nails can split. What happens with a horse if it gets a split in the hoof? I assume that it can happen, but I have never come across it.

Because of the shape of the hoof it tends not to split in the same way as human fingernails, but they can crack, chip and become inflamed underneath the hoof (eg laminitis).

In most simple cases, a skilled farrier can tidy it up fairly well, or they may need corrective shoeing for a while. It usually happens if the horse has odd conformation or an unusual way of standing for some reason.

Don't horses wear shoes all the time anyway? So unless they throw the shoe somehow, how could this happen?

And how is corrective shoeing done?

Horses do not wear shoes all the time, and many never wear shoes. It depends on what a horse is used for and sometimes personal choice. Corrective shoeing is normally where a different type of shoe is applied, sometimes with rubber pads to help the hoof grow properly or alleviate pressure/pain.

So the rubber would be used in areas where the hoof essentially needs building up perhaps? If so that is somewhat like corrective podiatry isn't it.

Not all horses wear shoes. Some never need them because they're on grass their whole lives.

Corrective shoeing can also involve lengthening the toe or heel out beyond the edge of the hoof to correct conformation. I don't have a diagram, but if you imagine a horse wearing a logn heel, then that foot can't drop down lower then it should and the toe cannot rise above the ground abnormally. They can be difficult to keep on the horse though.

I have some that are ridden and some that are not. The ones that are never ridden are free in a sense to run through the property and I never shoe them, no need. Be careful about their feet, I have seen people think they can shoe a horse, and end up doing it wrong. Once a person ended up with a nice vet bill for this mistake. If you don't know how, ask for help!

One of the horses I was given had a badly split hoof. It took 5 or 6 sessions with a shoer to trim and fix the foot so the horse was comfortable. It was sad, and it seemed like it took a long time to heal. Now she is super healthy and doing great.

I am almost stunned at the thought that someone would try and shoe a horse themselves when they are not skilled at the practise. That sounds like a recipe for disaster, and I am hard pressed to believe that people can be so stupid!