Hello,
I think the figure is meant to represent a trooper at the time of Little Big Horn.
The regulation hat at the time was the 1872 model, made of black felt; it had a curious (and not much used, it would seem, judging from his rare appearance in period photographs) feature, namely that the brim could be hooked to the crown making a chapeau-bras. It was a low-quality affair, which quickly lost its shape, and was frequently substituted with privately acquired models, in different styles and colours. Even straw hats were used.
HTH,
Dani