Wow! I think you are correct! Do you think it went on a saddle? Is it Civilian, and early 1800's? I found an old Colonilal Civilian Flat button in the same park.
Thanks everyone for all of the input. I visited a local tack shop, and they did not positively ID it as equestrian related. That said they didn't rule it out either. Please see a side view.
It isn't horse tack related...at least it's nothing I am familiar with. As I posted it reply to your "What Is It" thread, I think it is a contact from inside an old flashlight that would have taken D cell batteries. It has a definite rim around the perimeter, and the nipple looks to be a bit concave, which would have been caused by battery contact fatigue. The rim is probably a spring seat where the coil spring was seated.