Cob Home. With exterior of Stone?

I was thinking about making the exterior of my cob house look like stone, either by sculpting the exterior cob or by somehow using some local rocks ( which are all over the ground here!!) and mounting them to the outside of the cob. Good Idea? Will it interfere with the ability of the cob to heat and cool? Could I insert the rocks while building the cob house? Or would it be better to do after it had dried and shrunk?