From someone who does a lot of winter biking on pavement, but not usually on a lot of snow, what is the first thing I need to know about biking on snow, other than lower the psi in the tires?

Backup: I have an 22 mile round trip each day through suburbs / country roads and I'm discovering that a mild coating of snow leaves slush and ice on the pavement that is not getting cleared. This morning I tried biking on the shoulder where there was packed snow but I encountered some immediate fishtailing so I went back to the slush. Not sure if that's a long term strategy.