But first, a parenthetical note for those who are acquainted with Jerzy Kosinski's novel called The Painted Bird. Here's an excerpt that's oddly related to that from the Field Artillery Journal (November-December 1935, p. 537)—
[While awaiting orders to go into Mexico in 1915, the US 6th Field Artillery] had been instructed to leave behind any conspicuously marked animal. The favorite horse of Battery A was a big gray. The men were so anxious to take him along that they dyed him with potassium permanganate. The result was a dirty brown. It might have served, but when the dyed horse returned to his coral, his herd failed to recognize him and attacked him as a rookie. The gray won the fight that followed, but he lost most of his war paint.
Now back to the spurious zebras: As confirmed by a news photograph (above), early in WWI in East Africa, a band of British scouts under the leadership of Berkeley Cole (as described in Valerie Pakenham, Out in the Noonday Sun: Edwardians in the Tropics, p. 213)—
painted their ponies zebra-fashion with iodine to blend into the landscape, and spent five months leading a glorious cowboy existence, riding across a vast game reserve full of herds of almost tame game, before being brought sharply back to reality by a vicious fight with the Germans as Mbuyuni. Cranworth's zebra-striped mule, to his horror, bolted headlong through the German lines, and he then had to charge them in reverse.
Another confirmation of this (see photo below) was published in various US newspapers, such as in a story titled TRICKS IN ALL TRADES, in the Atlanta Constitution, on Sunday, June 13, 1915, with a caption that reads: English Troops in Egypt Paint Their Horses to Resemble Zebras, Which Are Almost Invisible Against a Tropical Background. In a concurrent but different clipping (with the same photograph), the caption reads: A British officer's pony dyed with permanganate of potash in order to make it less noticeable when fighting against the Germans on the East African border.
That said, consider three additional bits: According to Wikipedia, there is a tradition in northern Mexico of painting white donkeys to look like zebras, commonly referred to as Tijuana Zebras. In 2012, new research was published in the Journal of Experimental Biology claiming that a zebra's stripes make it less attractive to horseflies—with the result that some horse owners have since been painting black stripes on their horses.
More recent (if not all that surprising) is apparent confirmation in the journal Zoology that zebras' stripes may be confusing as they move.