Have you gone to the store to stock up on bread, milk and toilet paper yet?
No, never. I've been driving in winter for 40 years on snow and ice, real snow, not a dusting.
I have never had an accident, run off the road or any other mishap in foul weather - well came close once when I crested a hill, the road had all but been blown closed and was headed down towards a on lane bridge which was made of stone. I had no idea of where it was, had to use the snow bank to help slow the car and then aim for what i hoped with the dead center of the bridge.
That was with a front wheel drive car, not an all wheel drive truck. I figure worst case is stores will be closed for maybe a day, or two. I can survive that with what is in the house.
No reason to stock pile anything.