This will be my 3rd winter commuting to work 5 days a week on a bike, I have tried two kinds of bikes and FWIW at this point I prefer skinnier tires.
This is last years bike, a rigid MTB. I had high hopes, but I spent a lot of my time sliding and fighting my way through high snow.
This is my usual winter bike, a converted low end road bike. This bike manages much better than my MTB in deep snow, the skinny tires seem to find their way to the road surface.
Now on ice... both bikes are up a creek. We had multiple ice storms last year and I fell on my side 6 times. This year I am thinking about studded tires for icy days. Good luck on whatever you come up with. It will probably take some experimenting and maybe even a couple rough commutes to figure out what you prefer. No matter what, try to have fun with it.