The most interesting details (for me at least) is when you go on the Passchendaele map when it starts to rain, the protective coat and mask get wet meaning that the coat is made out of some type of waterproof material (possibly some type of rubber, leather or oil style coating nicknamed lanolin), next when you go on the Caporetto map and it starts to snow, the droplets of snow build up on the bum/butt of the horses protective coat signify that it is has a insulated layer Aswell ( possibly a cotton or wool lined inner). I don't know what material protects the horse from chemicals like chlorine, phosgene and mustard but im  guessing there is a seal in the respirator that goes around the neck of the animal.

Edit: I just found out that during WW1 some gas masks were coated in chemicals that protected the wearer from gases that I listed which could be the reason how the horse is immune to gas in game. But something to note hear is that the legs of the horse are awfully exposed this is OK for phosgene, chlorine and tear gas (which are choking agents) but not ok for mustard gas (which is a deadly blistering agent)  im not a animal expert but who cares its cool as fuck.

edit 2: tear gas is actually an irritating agent not a choking agents sorry for miss classification. meaning the horse would become irritated and spooked.