Why Wait(3)

As a relative Newbie to the game, I was wondering on what advantages can acrue through using 'Wait', when attacking another army. Two come to mind.

1) In the winter, the snow may clear improving the performance of archers. Also removes fog, with the same presumable benefits.
2) In the desert waiting until the sun goes up (presumably) might speed up tiredness in heavily armoured troops.

Anyone else got any ideas - or evidence?

Yes, it means "wait for different weather". As far as I know, there are no fatigue effects, except through the weather.