The loops are across the front of the short jackets. I assume they were some kind of gold thread, by the looks of them. William T. Martin was very fastidious about his dress and those of his command. These young men from Natchez and Adams Co, MS were all hand-picked by Martin himself because of their horsemanship, fearlessness, ability to shoot, 'standing in the community', etc. Of course, they were extremely loyal to the Confederacy, as well.
Martin even hired a Frenchman to teach them the basics of swordplay, but I imagine most of these men preferred sawed-off shotguns at close range.