Norway is pretty cold so your comments are due serious consideration. But it's counter to what I know. It's just basic physics. Also, you see it in the reg manufacturers who build "cold water regs" (mostly diaphragms with environmental sealing) but almost never cold water 2nd stages. For second stages, what you can do is put a metal purge cover which facilitates heat conductance w/ the relatively warmer water. That's about it. AL has a cold water 2nd stage in their glacier model but it's just a metal cover w/ an expanded metal hose adaptor to, again, to promote heat conductance w/ warmer water (low 40s/high 30s is cold but obviously not freezing). I have it but use SP S600 and Hollis DC212 which work fine in both cold and warm waters.
Was thinking of commenting on Storker's post as well. I bet diving in Norway and those conditions everyone there has cold water rated 1st stages. For those of us using basic unsealed warm water rated 1st stages, we are more likely to get 1st stage freeze. Sealing the first stage pretty much eliminates water in contact with any moving parts, so pretty much eliminates ice impacting first stage operation.
In effect both of you are right - with sealed first stage diver only needs to worry about second. For the rest of us, 1st stage is the big concern. I suspect that first stage freeze up also releases a much larger air flow - at the very least the same amount from each 2nd, but certainly both 2nds will free flow.
Given OPs story in which it sounds as though only the primary second stage free flowed, I imagine that the 1st stage only partially froze preventing total closure - resulting in IP creep - flow was small enough that primary second stage with lower cracking pressure was the only one leaking.
Still wondering how he was doing on air before the leak started and whether he was monitoring pressure sufficiently before incident.