The tyres you need in winter depend on the winter you have.
In the UK its normally cold and damp, maybe raining (less than you imagine) and very occasioanlly snowy and icy.
I use my slick 26x1.9"Big Apples all year round but this year when we had an extended freeze I made some studded tyres from cheap knobblies. I chose 1.75" for clearance.
Big wide unstudded knobblies may be best for rutted snow but overkill for anything else.