Use the Transform Shader in-between the Cloud Shader and its Density Shader and adjust X, Y, Z parameters for Translate and/or Scale (Transform would be best). This will move the noise function that defines the density of the cloud and thus the cloud shapes. Animating along the Y axis will move the noise function in the vertical, which acts somewhat like cloud "evolution" in practice.
Passable attempts at tornadoes have been accomplished (probably something would turn up in a search of the forums), but I doubt you could animate it convincingly.
- Oshyan