For Flyadive and anybody else who doesn't already know:
Although that brass object looks like a scabbard-mount, it actually is a horse-harness component known as a gag swivel, part of a horse's bridle. The one found by DanPM94 could be either a swivel or part of a gag chain, as shown on two pages from a 1907 and 1909 horse-harness & saddlery catalog, below. Also shown in use on a horse in the modern photo. Nobody has reported seeing one in any photos of civil war horses, so apparently they are a post-civil-war relic.