Although to be honest, around here we almost never have persistent (packed) snowy streets anymore (those usually have very good grip). The winters are milder with every year, so most snow just disappears in a few hours, and most cycle-paths and streets are salted heavily, so it is just wet most of the times.

The only really tricky situations were right in the middle of heavy snow-fall, where a lot of salt was already on the street or being added. The street is soap then, and I don't know if any tire will help you with that.

It is another thing if you live where there is a lot of snow, and often fresh powder - let's say more than 15cm soft surface on a regular basis. I guess yes, you would sink with most regular tires there, then you need large balloons and a bike that can take them.

So, those treated paths in Finland are almost certainly safer (from a slipping/sliding perspective) than the Mid-Atlantic US, where paths melt and refreeze throughout the day, leaving a slick layer on top.

Fenders and lights are essential.

(Edit: I'm in Germany; we tend to get snow and ice in winter and the cycle paths are not always cleared immediately.)