Try "bridle" rosette and you've got it right. It is either a rosette or similar leather horsegear accouterment/decoration. It had a brass wire for attachment embedded in its solder-filled back. That type (meaning, solder-filled) dates from the late-1700s through most of the 1800s. For civilian ones, if the front doesn't have a time-dateable emblem, there's not much way to tell whether it's from 1810, 1850, or 1880.