When we meet Fighting Joe Hooker he is smoking a pipe. The pipe was made by the British Buttner Pipe Co in the 1940s and is made of Bakelite with a porcelain insert. Later on Sugar is smoking the same pipe when he tells Monte about the Countess.
When Fighting Joe rides his horse off the cliff, the horse jumps into mid-air. No horse would consent to this. They have brains and they make judgments. The horse would make every effort to stop and not go over the cliff.