Kuger is correct. More specifically, your solid-cast brass US Army Great Seal horsegear rosette dates from around 1902 into the late-1930s, when the army stopped using horses for (almost) anything but Ceremonial purposes. (They are still used for that purpose today.) Yours is missing the brass attachment-bar which was on its back. The photos below show one on a World War One era US Army horseharness, and a "backview" showing the "staple-shaped" cast brass bar on the rosette's back, for attaching it to the leather straps.