Technically, it all is the same motion. The difference is magnitude and direction and how you separate out the superposition of them.
Temperature is a result of the components of motion (vectors) of each individual air molecule with a net translational movement of zero over time. This motion is random and all over the place in many directions as they move around, collide and bounce off each other and objects. This speed is apparently around 500m/s, just to give you an idea:
Wind is the collective motion of a mass of randomly moving air molecules: the average velocity of the actual motion of the individual air molecules. Averaging their velocities cancels out the vectors that point in "random" directions which lead to net zero motion, leaving only the collective translational motion remaining. Obviously, wind is usually not 500m/s.
So, typically, the random net-zero impact vectors between air molecules and objects are much higher speed than those due to the collective/average motion of the air molecules (wind). This means the net-zero impact vectors dominate over the translational impact vectors in kinetic energy transfer (heat) in either direction into or out of your body.
But if you're an SR-71 flying through the air at Mach 3, the relative wind speed is so high that the vectors of the translational motion of the air molecules is much larger than that of the net zero, random motion. The result is a net heating of the aircraft skin due to impacts from the wind even if the random velocities of the individual air molecules make for very cold air that would otherwise cool down the airplane's skin.
So a cold wind would be one where the kinetic vibratory motion (thermal motion) of the molecules in your body is higher than the random motion of the individual air molecules such that energy is transferred out of your body into the air from the collisions rather than into it, and impacts vectors for the average motion of the air (wind) is too slow to to transfer energy from the air into your body and only replaces the air molecules heated up by your body with fresh, cold air molecules.