I live and work in the city, so maybe it's different for me than for others.
I stick to the main streets since they're plowed and salted better. Side streets aren't plowed for a couple of days after a snow, which lets hardpack turn to re-freeze which is about the worst stuff to ride on.
Agree with this. I find also that immediately after snow I am the fastest thing on the road along with other cyclists! In winter on slippery roads you want to be taking the lane as cars can skid easily.