Here in Minneapolis, you see most winter-bikers riding with ski or snowboard helmets. Bern is very popular. My daughter uses her Bern snowboard helmet for winter-bike & snowboarding.
Snowboard helmets are designed to protect the back of the head more than bike helmets ('boarders fall backwards a lot). The forces from a snowboard crash are going to be similar to a bike crash. Moving speeds are similar, and if you watch a terrain park and the stuff kids do in there, you'd be fell safe enough on a bike using the same helmets they are bouncing off the hills.
I've tried using my snowboard helmets, but I get too hot. I use my year-round Bell Muni with a wool skull cap in the winter. I have stated in other winter bike related forums, I run hotter than most people .... Cold feels different to everybody, use what keeps you comfortable and warm.