The cremaster muscle in the scrotum helps to pull the testicles against the body in cold environments. This causes the firm and rigid scrotum response. This is done to keep your sperm at an optimal operating environment.
The penis is made up of spongy compartments that must fill with blood to become erect. In cold these compartments are minimally filled as vessels contract to preserve bodily warmth.
Your response is normal, though it sounds like maybe a little more exaggerated the most.
You must be doing a lot of cremaster curls in the squat rack.
