You're thoughts here are similar to mine. Infact, it is indeed 12° right now and I am in shorts and a t-shirt as I always am going to work.
The difference between running and bicycling is the speed. Moving 15 mph through the freezing air is much different than running speed.
My coldest was 18° on the bike, but that was because I had nothing else I could do but ride the bike or sit in the car at the lake. I had no where else to go at that time. I was on the bike every day from after work until I was ready to go to sleep unless it snowed, then I walked around aimlessly for hours.
I am always hot and it's not from the environment. Anytime I am working, my body is massively overheating no matter what the environment is. So at 18°, I was burning up sweating but yet on the skin surface freezing cold because I am soaked in sweat from the working. It definitely was very unpleasant.
It was neat though being out late at night when it just starts snowing. Very peaceful bicycle rides.
Windchill does come into play even with running, real wind and the wind generated from running.
I would think that it would be really unsafe out in the snow on a bike.
I got a pre dawn phone call from my neighbor a few years back. He had taken up cycling a few months prior and was taking a different route. He missed a turn and figured he would find his way back to the planned route without needing to lose momentum by turning around.
As he was coming down a hill towards a bridge he said it look different. Turned out it was a wooden bridge with slightly elevated places for the car tires. It was foggy and damp that morning. He hit the bridge with his tires right in the middle of the area for car tires. About half way across the bridge his bike just slide out from under him. The tires just didn't grip at all on the wet slick wood.
He ended up just off the bridge, barely in the road. He rolled the best he could until he was in the tall grass beside the road.
He laid there in pain and hoped someone would stop. It was pre dawn and a very lightly traveled road but two cars did pass. Neither stopped, they probably didn't see him in the tall grass. He finally drug himself to where his bike was about 5 feet away and luckily his cell phone was still attached to the bike.
He had to call me multiple times before my phone rang to wake me up. He sent me a map pin to his location and I went to pick him up.
If I did not know where to look I would not have seen him lying there in the grass. By the time I arrived he had been laying in the grass for 45 minutes, multiple cars had passed, none seeing him. I ended up taking him to the ER and his bike home.
Luckily his injuries were all muscle and bruise related and no broken bones or head injuries.