Totally possible, if you set up a heap of different day cycles and such
If someone wanted to take the idea, since I'm too lazy to make/tune day cycles:
At midnight, determine the weather for the day and swap to that day cycle/skybox.
Weather would be defined as current weather, new weather and a transition point. Such as clear to rainy in the morning, which would fade into rainy day cycle settings around the 0.3 mark of the day cycle, or rain to overcast in the afternoon which would be raining up until the 0.6-0.7 mark and then stop the rain, leaving the overcast skybox.
You'd do this so that instead of just SUDDENLY RAIN you could tune the environment settings to slowly make it more overcast, then at the 0.3 mark it swaps to the full rain skybox and starts the precipitation, etc.
The actual code is easy, mostly it's a case of making a heap of environment settings and setting them all up correctly. ie, a lot of monotonous busywork that can't really be made much easier by coding cleverness.
You can use Lugnut's (I think it was Lugnut's?) day cycle events as a code reference for firing something off at midnight, or any other time for enabling/disabling precipitation.
