Layer scrolling only works if your layout is bigger than the screen, and you are moving the camera.
Your game does neither of those things.
You can scroll the Tiled Background texture of the snow and trees the same way you are doing the clouds, by moving the offset, but you have to make your texture size a square power of 2. In other words, it needs to be 128x128, 256x256, 512x512, etc...