Guessing here:

This was not a cheap badge looking at size / construction. I am thinking European and maybe Germany / Austria / Hungary or the like based on similar looking work. Not recent either.

It seems to be a stylized horse. If curved enough to fit on an upper sleeve, I would further guess maybe an association with horseback sports. Boar hunting ? Hunting Deer with hounds ?

Alternately someone in charge of horses in a military formation