In the interest of horse-girl infodumping, I recall seeing some at the Gilcrease Museum in Tulsa, OK, and luckily they have some pics for their online collection, thank you Gilcrease.

This one is the one I remembered offhand, with a high pommel and cantle (turns out it’s not Cherokee): collections.gilcrease.org/object/84987

Here’s one that used antler for the pommel and cantle, which I thought was neat: collections.gilcrease.org/object/84984

This one actually has stirrups, looks like the girth attachments are more sophicated than my Dunning-Kruger ass imagined, but the stirrup leathers are, in fact, looped over each of the wooden bars: collections.gilcrease.org/object/84985