Which part is NOT typically found on a saddle?

The brow band is a component typically associated with a bridle rather than a saddle. It is the strap that runs across the forehead of the horse, holding the bridle in place and often embellished for aesthetic purposes.

In contrast, the stirrup bar is a part of the saddle that allows for the attachment of stirrups, providing the rider with a place to rest their feet. The cantle is the rear part of the saddle that offers additional support and stability to the rider, while a nose band is a piece of the bridle that goes around the horse's nose to help control its head and prevent it from opening its mouth excessively. Thus, the brow band is the element that does not belong to a saddle, making it the correct answer.