Pendants, mounts, and buckles.
Enamelled harness pendants, strap mounts, and bridle bosses are common metal-detected finds, often heraldic in the medieval period — a pendant’s arms can sometimes be tied to a family, which is as close to a name as a small find ever gets.
Pendants hang from a separate suspension mount; finding either half is normal. Note the suspension loop, rivet holes, and the gilding and enamel that survive in recesses.
Wear from movement against leather polishes contact points in a way display never does — a genuine riding pendant is smoothed where it swung.
Later horse furniture is its own family: crotal bells, hame plates, and decorative brasses run into the modern era. Record shape, any heraldry (colours as well as charges), and fixing method, and date by the decoration rather than the horse.