Nope. It comes down to the engineering design. If wind turbines are spinning in too high a wind, above 55 mph, that can cause damage to the comparatively delicate rotor. When the blades are locked in one position, the rotor is safe, and the tower and blades are strong enough up to handle winds up to about 150 mph.
Of course they still need to keep the generator and machinery warm so that requires power even when idle.