I wear a Kali road helmet year round for both on and off road cycling. As the temperature drops I progress from ear muffs to a nomex NFPA 1970 (structural fire fighting) rated balaclava, to a Cold Avenger, and finally the Cold Avenger over the balaclava.
I also have a yarmulke under the helmet all the time, but I doubt that it adds much warmth.
I haven't looked at the standards for ski helmets vs bicycle helmets, but I would guess that they reflect the higher speeds on skis and the tendency for ski crashes to be on a softer surface than concrete. Also, because they tend to be on steeper inclines, the ski crashes I have seen involved multiple impacts.
I do wear a hockey helmet for white water kayaking and I know that they have a much more rigid shell, and mine uses a gel that works for multiple impacts. I wouldn't wear it on a bike.