A hoof pick is an implement for scraping mud, stones and manure out of the bottom of a horse's hooves. It consists of a curved piece of metal about the size and shape of a medium-sized phillips screwdriver, but bent into a J shape, with a handle of some sort on the long side. Some hoof picks also have a small, stiff brush attached.
A horse's hooves are usually picked before and after riding. Since the hooves of a horse are essentially nothing but a huge bony nail, rather like an enormous fibrous fingernail, this process is painless to the horse (though it looks alarming the first time one sees it done). To pick a hoof, you stand beside the horse, facing the rear of the animal, and run your hands down its leg to the ankle, perhaps leaning into the horse a bit to take some of the weight off the hoof in question, and then grab the horse by the ankle and lift the hoof so that you can see the underside. (A well trained horse will cooperate with this procedure.) Then you use the pointed end of the hoof pick to remove any mud or other debris from the bottom of the hoof until the fibrous frog of the foot is clean. This process, repeated daily, prevents stones and other sharp objects from becoming embedded in the hoof, thus perhaps making the horse lame.
To avoid being kicked by the horse while performing this service on the rear hooves, it is a good idea to stretch the back leg backwards a bit, and brace the hoof on one's knee. To kick, the horse must cock its leg forward, which this maneuver prevents. I have seen a horse trainer jump up and kick a horse sideways when it tried to kick her while she was picking its hoof. (The horse was quite surprised by this, and thereupon decided to be more cooperative.) Disciplining a horse to tolerate having its hooves picked is an essential part of horse training.
Wild horses survive in spite of not having their hooves picked largely because the horseshoe, in the domesticated horse, is responsible for catching and retaining much of the material which picking removes, and of course wild horses are not shod.