If you've read my weapon animation hacking document you probably noticed that bows and arrows have their own palette assignments, but only the arrow's palette is usually seen in the SNES version. It turns out this is only half true, if you equip the arrows in a character's right hand the arrow palette is used, but if you equip the bow in the right hand the bow's palette is used instead. Only noticed this because a save I downloaded had Rosa's bow and arrow reversed.
This does not apply to the GBA version where the bow's palette is always used, regardless of which arrows are equipped.
Edit: Did some further testing. As I figured it's not just the palette that changes but the entire animation. A functional bow and arrow combination animation requires one weapon's fourth byte set to 04 and the other weapon's set to 05, it doesn't matter which one as long as both are used, otherwise you'll just get a normal attack animation. If the weapon in a character's right hand has its fourth byte set to 04 or 05 and the other weapon doesn't have the correct byte the character will use the punching animation instead, the combination still functions perfectly and the damage done is correct.