Color dithering/quantizing

For stylistic purposes, I'd like to have a game engine that can render landscapes using a dithering effect, similar to the following game screenshot:

I figured the easiest way to do this would be to change the game to 256-color mode... but I can't figure out how to do this.

Of course, the best-case scenario would be if I could choose between having a dithering effect on a model (similar to the dunes in the screenshot) or a quantizing effect (like the car in the screenshot).

Is there a way to accomplish this type of low-color effect in Unity? Is it possible that I could write a shader to do this? (I have no experience with writing shaders but I'm willing to learn)

8-bit screen modes are increasingly unavailable in modern computers, so that wouldn't be desirable even if it was possible. Some kind of full-screen image effect would be one way to do it (requires Unity Pro). See here for someone's start on a posterization shader.