I can't speak to battles of antiquity - which it seems your post is pointing towards - but I can give you some interesting stuff about WWI. I recently did a project based in sketches, paintings, and other selected visual media as a barometer for understanding soldier experiences in the war. while the paper had much more breadth than just the encounter of nature and machine, that was one aspect that struck me particularly. Allied artists (not official ones, guys who were drawing/painting from the trenches), had a real fascination with dead horses - it was always representative of the chaos, the shock, and the raw destruction of nature. that brought me to some secondary research about the prevalence of horses (and other equine species) in the Allied forces. in the end, I found that there were an estimated over 8 million equine deaths during the conflict, equalling the amount of civilians and combatants individually. the animals were crucial for forward supply, artillery units, and even some mounted units (not to mention correspondence) and the war could not have been expanded the way it did without them. in this sense, even the first modern war was highly dependant on animals and were seen as one of the more important aspects of the war-machine.

take a look at some of Otto Dix's stuff or even some of the works collected by the Canadian War Museum. it's really quite interesting to see horses - and nature in general - assume such an important part of soldier-produced art.

Many tellings of the Battles of Crecy and Pontiers during the Hundred Years War indicate that yes, horse casualties were significant; archers sought to enfilade cavalry formations, and hit horses (large targets difficult to armor completely) in the sides, where they were generally less armored. Mass weapons, like pikes, halberds, bows, crossbows, and guns didn't make much distinction between man and horse.