I will go with my Dad's answer "Heroes do not shoot horses". Long ago watching a western with my dad, group in stage coach being chased by bandits. One of the heroes was on top of the stagecoach using a winchester to shoot at the bandits. The movie was semi-realistic in that he was not having much luck bouncing about. I asked my dad "Wouldn't it be easier to shoot a couple of the lead horses? Horse falls, trips those running behind, bandits get tossed and crushed." Dad looked at me a bit disturbed his 10 year old would think in those frames and replied "Heroes do not shoot horses"
Josie Wales was a hero.
Ergo, he does not shoot horses.