I rode all through Essex winters with my trike.
It’s fine cycling on ice unless it’s very hilly, but you can easily have drive wheel traction issues.
My former husband and I were doing doughnuts on an icy road once for fun and he rolled his QNT!
If the snow is more than 1cm deep then it’s really hard going pushing 3 different wheels through it.
In my Velomobiles which are heavier you can ride in thicker snow as there is more weight on the drive wheel and I run super-skinny front tyres in my Milan but there you have the problem that snow is scooped up through the foot holes.
I cycled to work on Wednesday with a half centimeter layer of snow on the ground. This was because I am really unused to driving a car in snow and my current car, an SLK, has rear wheel drive, fat all-weather tyres and a big engine. So I decided my lack of experience driving in sno meant cycling was safer. If I only had two wheels I would have taken the car. I was the only person who went to work by bike that day - normally there are 7 of us. Three wheels good.