I wouldn't recommend a scooter for winter commuting especially under icy conditions. It's probably not what you wanted to hear, but a bike you can fit studded tires on would be the way to go. Alternately, walk and use crampons if it's really icy.
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None. Look for a bike with a wheel size where studded tires are available. A bike with fat tires might also work.
In those conditions, I'd only feel safe on a large tire bike with studded tires.
I put my Max away for the winter.
Scooters are not great for icy/snowy conditions because you can't fit studded tires and cold weather can impact range pretty significantly: Most people I know just don't use their scooter once the weather gets bad enough.
Personally, I stick to bikes and would recommend either an unpowered bike that can fit thicker tires or an ebike with fat tires. For icy conditions, studded tires are recommended. If you're only dealing with snow, then thicker tires should do fine.