A couple of advantages that I know of, though there is probably more:

1) Some generals get an extra command star or two to attack at night, you can see this difference by clicking on or off the 'attempt night attack' box. No brainer, if you are using one of these guys, always attack at night.

2) Re-enforcements can't join a night battle unless the are commanded by a general with the night fighter attribute. This has HUGE implications.

3) I'm not 100% sure this is accurate, but it seems that the change in visibility not only affects your ability to see enemy units, but also the AIs ability to see yours. I fought a battle in Scotland recently where it was night time AND foggy/rainy. I outflanked the enemy with 2 units of knights, and rather than repositioning spearman to face them, which is what the AI usually does, the enemy seemed to ignore them. It seemed this was due to the fact that it was low visibility and a night fight... but I don't know how to confirm that it did indeed have an effect.