Wide cheesy tyres running at about 10psi (and no brakes to speak of) seems to be the secret.
It is essential to have the plastic V-brakes flopping out sideways and the rusty cable tied to the bars. Wheel braking (as opposed to foot-braking) is a major cause of problems when riding on ice.
My preferences for snow and ice riding are the following. Proper ice is something else, but never encountered on my regular commute in over 20 years riding.
'cross bike, with regular mud tyres run soft. Pretty secure-feeling on compacted snow, but maybe I've been lucky. Don't touch front brake.
'cross bike with studded tyres. Obviously.
Brompton. Drop saddle real low and use feet as outriggers on descents. Platform pedals allow for rapid foot-dab response in likely case of small-wheels squirming all over the place in snowy ruts. Not far to fall, can also bail out and get train. Don't touch front brake.
MTB with soft kobblies, drop saddle as above. Best you can do if you don't have a BSO of your own (why not? snow bike for the price of a saddle). Don't touch front brake.