PA-dirt_NC-sand's answer is correct, but not broad enough. Those copper rivets were used on horse-harness but also many other leather objects, such as luggage. Ones with a raised 5-point star on the disc was made by the Plume & Atwood Manufacturing Company of Waterbury CT, reportedly from the 1920s through 1955, when a flood almost destroyed the manufacturing facility, which eventually got sold to a new owner. The star-mark rivets might date back earlier than the 1920s, but not from the civil war, because Plume & Atwood was first incorporated in 1880. Credit for the star-marked rivet ID goes to my esteemed colleague Nhbenz, who posted the attached photos here in the What-Is-It? forum several years ago.
Note that some have a raised anchor on the disc, also from the Plume & Atwood Mfg. Co. box, are shown in the closeup photo.