Which piece of equipment is designed to curb or eliminate self-mutilation in horses?

The cradle is specifically designed to prevent or minimize self-mutilation behaviors in horses. This piece of equipment typically forms a protective barrier around the horse's neck and is used to keep the horse from reaching certain areas of its body, particularly its legs and belly. Self-mutilation can stem from a variety of reasons, including stress, boredom, or health issues, and the use of a cradle can help alleviate such behaviors by restricting the horse's access to these areas.

In terms of the other options, a muzzle is primarily used to prevent a horse from eating or biting, which does not specifically address self-mutilation issues. A girth is a piece of tack that is used to secure the saddle on the horse's body, while a halter is used for leading and tying the horse; neither of these pieces of equipment are intended to curb self-mutilation behaviors. Thus, the cradle is the appropriate choice when the goal is to address self-harm in horses.