I talked about equine heart rates - but you can't exactly put your fingers on a horse's wrist.
In fact, the normal place to check a horse's pulse is under the jaw. There's a facial artery that runs below and slightly behind the front corner of the eye that happens to be quite handy for this. It's generally the easy place because it's easy to immobilize the horse's head with a halter.
Two other places that are sometimes used are the back inside of the knee and the inside of the ankle on the front leg (which is pretty close to the wrist).
However, it can be challenging to take a horse's pulse properly, especially if they aren't being particularly cooperative. For this reason, a lot of horse barns have a stethoscope, and listen to the heart directly - you put the diaphragm just behind the elbow. This is also what most vets do.