I have been giving this some thought myself - I'm afraid I can't be a world of help with the skybox thing, I have usually used a sphere for this, but on the weather pattern thing I have tried to think through a route to having it work.
I think the best way is to use a Texture-By-Reference to map the skybox and use Java2D to generate the actual image. Now I think about it, it may be a lot easier to do this using a square skybox because otherwise you need to sort out sphere mapping as well as any changes to the image itself.
I would suggest using a standard day/night pattern with straight blue-sky through to starry night and then overlaying a plasma cloud pattern over it. It may even be smart to alphablend the layer and place it on another shape inside the skybox to create some degree of parallax, but it may be as effective and more efficient to merge the two layers into a single image.
If you're not too up on them, plasma patterns are often used in fractal terrain generation - there is a good tutorial page here