@7thWisconsin Not any kind of expert on this but it is my impression that a sabretache was a flat leather bag suspended by straps, usually 3, from the same belt as the saber and on the same, (left), side as the saber. It was generally worn by light cavalrymen, especially hussars. I believe it originated in Hungary but was used by light cavalrymen of most European armies in the 18th. and 19th. centuries. If I'm not mistaken its original function was to carry dispatches in however it often got used to carry other things. Officers versions could often be very ornate. The ones used on campaign and by enlisted men were often much plainer but frequently sported the regimental number or some other martial device. I have the impression that they became something of a symbol for hussars and a traditional part of the uniforms items that set them apart from other, less exalted light cavalrymen.
I could be wrong but I don't believe that U.S. cavalrymen ever wore them.
John