Winter hit very suddenly on Monday here. It went from 60 to below freezing in like an hour. I drove to work on Monday because it sounded like there was a chance of cold rain, which is no fun to bike in. It turned out to be just snow, and the roads didn't freeze until night.
Tuesday it was 16 on the way to work and 12 on the way home. I wore my normal work clothes (jeans and a long sleeve T-shirt), hiking shoes that resist the wind just a little (they are not waterproof or wind proof), wool socks a fleece, an old synthetic jacket, a hat, helmet, neck warmer, and ski gloves. The paths were really icy under the snow because they froze while it was wet, but there was some texture to the ice. They plowed the paths, which made them more slippery since it smoothed out the ice. I ended up having to go super slow, less than half my normal speed, and I was riding in fear of falling the whole time. I had a close call going in a straight line where it was completely unexpected. I got cold because I was going slow and out there too long. (about 20-25 minutes?) Mainly my face and hands were cold because my face was uncovered, and these gloves are not that great any more. The ride home was about the same. I wore wind resistant pants on the way home, but they didn't help. I need insulated pants for this weather.
Today it was around 3 degrees all day, so I drove to work. It could get down to -11 tonight, so I'll drive tomorrow too. I might be able to bike on Friday again.
I've found that if it's above 25 degrees in the morning it's not bad to ride to work. Above 25 I'm warm enough in jeans and regular shoes, and I wear a hat, gloves (ski gloves or fleece gloves depending on the temperature and if snow is expected), a medium jacket or a combination of lighter jackets, and a neck warmer (fleece tube that goes around your neck).
Last year I rode on a 9 degree day wearing all of my ski stuff. Waterproof bots, wool socks, lightly insulated ski pants, a good jacket, hat, gloves, neck warmer, ski goggles, and maybe a face mask (I can't remember). Riding with ski goggles is awesome! That time only my feet were cold. It's too much work to do on a regular basis, though, because it takes time to layer up at home and take everything off at work before I overheat.
I placed an order for one studded tire for my bike. I was going to put mountain bike tires on it, but we get enough freeze-thaw days that there are icy spots that stick around for a few days a lot of the time after it snows, even if the snow melts. Water runs from melting snow onto the path then freezes overnight. I've had enough close calls and falls that I don't want to risk it any more. I'll put the studded tire on the front and put the better of the two regular ones, or a mountain bike tire, on the rear. If the rear slides out it's not as bad, but I'll consider getting a second studded tire if this one works well.