It is a US Army horse-harness insignia/accouterment, from the early 20th-Century. It is simple stamped brass sheetmetal, with two or three "tabs" on its rim for attaching it onto leather. Some diggers call it a rosette, but rosettes have a bar on the back for attaching onto straps, and this insignia doesn't.
Edit: Bryanhashemi and I were typing at the same time.