This sounds obvious but how would you animate the background scrolling into the distance like here? https://youtu.be/UtKFTfwLMhA?t=3m15s
That background in OP looks like it was made in 3d and then composited with the animation of the inside of the car.
I agree that this appears to have been done with a 3D composite. I downloaded the video and advanced it very slowly with my trackball wheel. You can see the side of the cars as they pass then you only see the back ends in the distance. I think you could do the landscape with three 2D planes and as a cheat I would not include the passing cars. The sky has no form and is just a gradient making things a little easier.
I agree with Ampy here.
I think the snow being very lumpy and textured might be a little more difficult to do as a multiplane, but perhaps to make it look like it’s going into the distance, one could use a quadmap on the layers to make them look like they move away from the camera, and the layers underneath could be moved with a peg inside the quadmap.
I think the cars moving in the other direction are fast enough to maybe get one drawing where it’s seen a little more from the quarter back view and then just switch over to the back view entirely.
For the road, I think just having the lines of the road invert cut inside there would be fine and easy to do : )
Once you get one full sequence of it, perhaps you could try to get it to loop, especially if it’s a very long scene.