[@Mattchstick] You can always just stick the arrows in the ground or stick them in your belt. Usually young boys who needed to come out to war would carry the arrows from the carts to the longbowmen. Quivers are a more recent invention (from when archery came back into style as a chivalry thing). Bowbags were more commonly used, which was basically a leather-reinforced sock - the belt of the archer actually held the arrows.

Sorry, I hope I'm not being critical or anything like that - I just know a lot about warbow use. It's quite fascinating!