The comment above about remembering you are not wearing crampons is very valid.
Make your own screw-shoes with hex-headed self-tapping metal fastening screws. Remove them again in spring and you will not find the holes after a week.
Google it.
They really work on ice, and are OK to pedal with flatties.
I made my own snow-ice tyres starting with a pair of Tioga XCs and added 100x stainless steel pop-rivets with steel washers outside the tyre. Deburred the inners and coated with nail varnish. Fine with standard inner tubes, but I would not chance the supersonic variety.
Remember, you need knobblies to grip snow and studs for ice.
PaulD