In LeFebure's book Riddle of the Rhine: Chemical Stategy in Peace and War, the author explains one reason why this might be so.
By the end of the war, the chemical environment had become so difficult that the mask filter canisters had to be pretty thick. But thick filters meant impracticably heavy masks, and increased the difficulty of breathing (unless the surface area could be increased). The British solved these issues by migrating the respirator to the soldier's chest, connected to the mask by a rubber hose.
Germany could not duplicate this method -- they lacked enough rubber!
LeFebure claimed that the Germans only barely managed to squeak by using masks with enlarged canisters of various filtration materials, but had the war continued much longer, with the British introducing new agents or increasing the typical tactical concentrations of existing agents, the Germans would've found this insufficient.
And without enough rubber for hoses, thus being unable to use chest respirators, they'd have been up shite creek.
Now, normal masks required at least a little rubber. With sharply-limited supplies, I suspect this had to be reserved for the soldiers' masks. Masks for large numbers of horses probably just weren't in the cards.
Edit: I misread the OP, and thought we were discussing WW1. I leave my post as-is, because for all I know it might have some bearing on WW2, as well. My understanding is that natural rubber (of which Germany had little in WW2 also) makes a much better flexible, airtight material...