Night fighting can give your army the advantage if you turn off the special, flaming arrow option (yes, I know it looks nice). The AI always uses Flaming Arrow as default

For archer heavy armies the battles usually start with missile exchange. Normal arrows are more accurate, therefore do more damage and kill faster.

In a one to one shoot out between archers using normal and flaming arrows, The unit using flaming arrows always routes first. The damage done by the flaming arrows moral penalty is less than the moral penalty from the extra kills of the normal arrows.