Lower gravity does not slow down arrows it makes them take longer to hit the ground. If anything the density of the moon being less then arrows would go faster.
yeah, the arrows fly as fast, but their arcs are less pronounced. E.g. it's like with the real moon buggy, it didn't actually go slower than it would on earth, it just falls more slowly when it hits some bump.
Actually, for all realistic purposes, the arrow would be faster. Less weight to it. But even more realistically, it's never fire at all, since you can't have wood in a vacuum. So, I'm just gonna be thankful I can actually dodge them.