Why is CL/Cd equal to L/d?
The frontal surface is indeed used for the drag coefficient of cars.
For airplanes, however, almost* all coefficients use the wing area as their reference. This makes sense exactly because it allows to express L/D as c$_L$/c$_D$.
* For the nitpickers: Control surface hinge moment coefficients use the area of their respective control surface, not the wing surface.