I once challenged myself to cycle to work every day for a year when living just outside Sarajevo, which is chilly in winter and at that time was inadequately cleared because of internal political differences.
As winter came, I gradually started to move from the back routes (uncleared) onto the 'snow-cleared' roads.
Soon after that (and to my regret) I moved onto the pavement in places for my own safety.
I rode an old POS/MTB I bought from a PX.
Tyre pressures were critical, but I have no idea of the figures.... they were best on snow when it was about 'that' hard to squish them. I imagine 40-ish psi.
Ice is simply terrifyng (I had no studs or spikes) and the best I could do was stay in a straight line and not touch the brakes.
A good sense of balance is important, as is being used to the bike you're riding and used to its habits and vices.
The only major problem I had was one morning when both the (cable) V-brake levers seized. It was like dying in slow motion.
I eventually skidded to a halt on the soles of my shoes to find that both cable inners had frozen to the outers. I think they'd got wet with slushy snow the previous evening and frozen in my porch.
It took both hands on each lever to break the ice. That was after I'd stopped... After that I kept my cables in very good condition.
I also did a 'Hoogerland' into a barbed wire fence one time on ice, but although I tore my trackies to shreds I had not a scratch on me. I still don't understand how.
As to hills, that really is asking for trouble in snow or ice. Even getting up them in the cold is nigh on impossible. Descending is an act of faith for which I lacked the necessary courage.
Even if you're on soft snow and your tyres dig in, you will probably have limited braking (I was on rim brakes).
This was, I should add, not UK-type winter weather, but usually around -12C, dropping to -17 ish in the early morning.
My conclusion (having done the year on a bike) was that rain is better than snow and sun is better than rain. This conclusion was based on perception rather than empirical analysis, but I stand by it.
I didn't wear a helmet for that year. Had I done so, my risk perception would have been dramatically altered and I'd be dead now as a result of over-confidence. Perhaps. Or something.