I probably would have answered "cool gray," but I would have been wrong.
In fact, all the swatches above are from the shadow side of the same building from a single photo. They range from dark green to pink to gray. It's hard to imagine mixing those colors and making them look right.
Did any of you answer "It depends?" If so, you had the right answer.
So what does it depend on? For one thing, the shadow side depends on the color of the sky. It's bound to pick up some of the blue color from there. But the reflected light from adjacent surfaces can be a huge influence, too.
If the reflected light is powerful enough, it can be the dominant factor.
In the photo above, you can see where the four swatches came from. The first swatch came from the top of the near plane. It's greenish because it's getting blue skylight plus green reflected light from the grass. That pink swatch is getting red-orange reflected light combined with blue light. Swatch #3 is lightened considerably by the white reflected light.
And area #4 is slightly more yellow-green than #1 because it's got a wider zone of grass reflecting into it. Here the limits of the camera's sensitivity fails us. The human eye is far more sensitive than the camera, and if you were observing and painting the scene, you'd see and paint these differences even more dramatically.
Read more about vertical surfaces in shadow in my book Color and Light: A Guide for the Realist Painter.
Vertical planes in shadow
A whitewashed wall in shadow