I cannot see an entire society doing this, in areas that range from small towns to medium sized cities.
The wind doesn't cut through proper clothes. I try to avoid the roads as well, but the bike paths work well where I live, even when the temperature goes down to -20°C.
Please try it again it's not really the same experience if you choose to do it. All your problems described above are easy to solve, if you have resources to buy a car[1]. Ice bark roads are navigable with cheap winter tires (it does take you 40% longer to traverse though). I need to have a change of clothes and layers. good gloves, shoes and socks are vital below -12° if you bicycle for and 1 hour in such conditions it's going to hurt alot.
[1] You might need to sell the car though, which might not be an option, but in the long run you should come out ahead
I assume that the parent post meant 0°F which is around -18°C.
This is highly dependent on your location and life circumstances. I live in Eastern Europe, have resources to easily buy a couple of cars, yet choose not to. I prefer to walk or cycle.
> People talk about bicycles, but 0 degree or snowy weather makes that horrid
In Amsterdam, people cycle in -10°C when there's 10cm of snow on the ground (I did so myself). While a little unpleasant, apart from walking it was the only viable means of transport: the metro and trains were cancelled because of snow, and cars and buses were mostly stuck in traffic jams because there were so many crashes everywhere. (Someone tell the Dutch about winter tires!)