I started by doing "dotty" clouds. I knew these wouldn't need clever lighting to look believable, and I had a few pictures which I could use for this purpose.
By using two different sets of UV coordinates, I was able to use top-down style mapping for overhead clouds, as well as ring-style cylindrical mapping for horizon clouds. One of the channels was used to break up the obviousness of the repetition by tiling at a different amount. Combined with the existing fog, the result was pretty satisfying and much nicer than just a plain sky, albeit nothing fancy:
For the overcast texture, I slapped and stitched together many different stormy and overcast cloud pictures. The fade in for this is simply linear, which is not very realistic, but I was in a bit of a rush at this point, so it had to do. I generated a normal map, which is mostly ineffective, but again... it had to do.
At night, the clouds are very hard to make out (which is about right), and they block the stars (also, about right). I would have really loved to add a moon which lit up the clouds, but given my failure with getting the sun to light up the sky, I didn't even try for the moon.
I set up a light function to give the appearance of the sun casting the shadows of clouds on the ground. The effect is very subtle (perhaps unnoticable? :S) but hopefully it gives that can't-put-a-finger-on-it extra dynamic "alive" feel to the lighting. This actually introduced an unexpected problem - because I had now started using the sun to light up the clouds, I was now casting the shadow of overhead clouds onto the clouds, which of course was nonsense. This actually meant I ended up duplicating the sun light without the cloud-shadow function and using that to light the sky instead.