English war bows typicly had a draw weight of 140 to 160 lbs, i emagine Legolas, being an Elf, could have pulled that without much strain, 130 lbs would rip through metal plate armor and 160 would most likely rib througn the body of one who had armor on.
i think that the body of a winged steed would probably be equal to that of steel plate armor(if not greater) so adding the height, and gravity, a 150 lb bow would probably kill it.
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