Horse shoes come in about eight sizes. and they SHOULD be fitted to the hoof
However, there is a style of horse shoeing called "cowboy shoeing". It's an awful method. A size of shoe was selected to fit outside the white line, the shoe was nailed on, and the hoof rasped off to fit the shoe.
This method is NOT good for the horse! This style has not died out yet, but it's on it's way out.
Most of the time, shoes are shaped cold, unless shaping a shoe for a specific problem. Forging, changing the gait of the horse, or some malady of the hoof.
Odd shoes are fairly common. Draft horses need shoes, burros need shoes, and oxen need shoes. By the way, busy bulls also need oxen shoes. But only on the hind feet. their hind feet get sore during a busy breeding season.
Most of these shoes need to be hand made. These are done hot.
Mules, burros and donkeys, have different shaped hoof. Most of the time, a regular horseshoe can be bent to the shape needed.
90% of the time, mules, donkeys and burros are shod on their rear feet only. Even shoeing half of their feet, is a whole job. They do NOT like their feet to be handled! Often the farrier must cause pain, by twisting their upper lip, or by biting their ears, to get their mind off their feet.(They really don't like their ears to be handled either!)