Do they conduct heat or hold it? They can't do both. Take two pipes. One metal and one plastic. Stick one end in ice water and hold the other end and tell me which one feels cold first.
Now put your mouth to the end of each and start exhaling through them. Which one (still) feels warmer in your hand?
What reports have you seen of 212s freezing up, other than the one I posted here a year and a half ago?
Having a heat sink on a first stage makes sense. The only source of warmth it has is the surrounding water. But, the second stage has a constant injection of 98 degree air. Why would it be good to maximize conduction of that warmth from the inside of the reg into the surrounding water?