I wish the article had gone into Friðþórsson's breathing a bit more. It seems like this and/or his body fat are what kept him alive.
I agree to all of the things you said, once you get used to the cold showers, in fact you would want more and more cold water running over you. More cold will get to be fine.
However, one thing I find annoyingly bad, given the time of the year is that I feel by body warmer (and feel that I might run a fever) and had to check temperature couple of times to see it is only normal. Not sure if this is going to be a long term thing or I might get used to it eventually.
I'm currently only taking cold showers, this is the third time I've started doing so. The very first one was quite an experience: my vision turned gray for a few seconds, I couldn't breathe, and I nearly fell over. The next day's was a little jarring but tolerable, and it kept on like that, a little less each day.
Then I fell out of the habit. My second and third times getting back into it, I didn't experience nearly the same drastic physiological effects, it was Day Two over and over again.
Right after the shower, you'll get super warm, even in winter. You're system just gets going to equalise your temperature.
Also, you'll be woken up no dithering about in a stupor until your coffee kicks in, it definitely gives you a kick in the backside to get going, so even just for that, it's worth it in my opinion.
And, I never get cold. I can work outside in a t-shirt in winter (UK winter) without feeling any cold.
Edit: Forgot I also heard about it promoting an energetic response in the body (starting your engine for heat) to wake up for the day ahead and start burning fat before your first meal. I heard Tony Robbins talk about an ice room or something similar in his house that he uses for that. Probably not ideal for night time showers.