E-scooters are reasonably stable when there's a small amount of ice so long as you don't use solid tyres. They are more stable than road bikes and city bikes because they have a wider area of contact with the ground. For more comfort, you can under-inflate the pneumatic tyres or buy studded tyres. Also, you feel steadier on them than on a bike because you always have one foot as a third point of contact if you need it, and you feel somewhat more in control than with a car as the inertia is lower. The battery life and dirt/sleet are more frustrating.
Don't knock it till you try it. Though be careful for the first time if you do try it, use common sense — drive slower and don't turn as sharply, dress appropriately as you'll be caked in mud. But otherwise it's doable and quite fun.
I've driven a bicycle in winter and yeah nah, I'd rather just take public transport. It's not just traction but the fact everyone else got shitty traction too, so there is a good chance than most of the agility of small bike/bicycle is negated by just slipping.
At least with bicycle like 95% of my route is not on actual road sharing it with cars, can't do that on bike.
That's honestly lesser problem than the fact 2 wheeled vehicles on ice are fucking scary to drive