Yes, I wonder that also. I live close to Dyche Museum at Kansas University, and they have Commanche, the only living thing (well he wasn't, there were other wounded horses) found on the Custer Battlefield. They did a great job and he looks like you could just throw a saddle on him.
In Joe's (Actually he went by the name of Little Joe) I would think he went into a museum and may, ironically, have been destroyed by fire at some later date. But I'm going to continue my search and see. According to the newpaper account, Little Joe and his partner (name unknown) appeared in London and other places after winning some sort of contest. Further I Knoweth Not.
Jon