Hi Sebastien,
Thanks for your question. You're not doing anything wrong or missing an option to see animation of the terrain and clouds as you've described.
The 3D Preview updates each time you make a change to the scene, unless you've paused it via the Pause button. Notice the text displayed above the 3D Preview pane that indicates how much time it takes to generate the terrain deformations and shading for a particular frame. It's not really possible to display these calculation in the "near real time" that you would expect to see by pressing the Play Animation button. As you've mentioned, the rendered frames are fine, and if you scrub the timeline and stop on a frame, the 3D Preview will start to refine the terrain at that time point including any deformations.
It's similar for clouds, accept that the 3D Preview can do a little bit better job at keeping up, provided there's not lots and lots of cloud layers. If you enable the RTP button at the top of the 3D Preview and press the Play Animation button, you'll see that the clouds try to keep up with the timeline, although it's very pixelated until you stop the playback, at which time the 3D Preview will continue to resolve the display to its maximum amount.