The wire looks familiar and is bugging me. I believe it's a clip and not a tool, perhaps to hold a lens or cap in place. I also think it's more recent item than to be from the mid19th century.
I just have trouble thinking a thin piece of iron wire would not have melted away over 160 years unless it was under cover from the weather.
My grandparents lived on a Butterfield stage stop at Cow Springs, NM. It was the next stop west of the Hatch River stop.
I've done as much research as I could years ago on the subject and though I'm no expert, never heard of mules being used on the stage runs. And runs they were, the mail was given only 25 days to travel the 2800 miles from St Louis to San Francisco.
From memory I believe teams of six draft horses were used and were run the entire distance from stop to stop where fresh horses were hitched up and the previous team given a day off.
These days I drive horses and mules for recreation and can't imagine running the mules more than a short distance.
Mules just aren't built for running, they have straighter shoulders and walk on a shorter appendix than do horses.
Mules along the route pulled freight wagons to supply the stops with everything from hay to hash browns. One of these may have lost that shoe?
Working the animals every other day also fits and keeps them in good shape without breaking them down.