Just to clarify, a skybox is a cube with the normals pointed toward the inside. A sky texture is applied to the cube.
Similar to that is a skysphere. Basically the same thing, except instead of a cube, it's a sphere.
The textures on these will usually be just a sky color (if you plan on using animated, 3D clouds) or a full-on sky unto themselves with clouds and a sun painted onto them.
Either of these could easily be supplemented by other 3D objects (moving just inside of them, near the top) such as clouds, spaceships, and whatever else might be flying in your sky.
Usually anything on the ground, such as glaciers and water as you mentioned, is not part of the skybox but is a seperate object much like the flying objects described above.