regarding colored bows

i havent played awakening yet but i do know that in fates bows were green. idk maybe just a hunch but what if colored bows became game specific? like FE_ and FEF gave us only green bows while FE_ and FE_ gave us only blue bows and so on?

something that doesn't really sit right with me tho is that for bow units, swordbreaker was usually the popular b slot so i cant imagine green bow units being so useful