In your situation i’d talk to your neighbours to see how things have been in the past - how quickly are the roads ploughed? How far away is the nearest shop and how long did it take to run out of milk/bread etc? If there’s a powercut, does the utility company manage to get out the same day or could it take days to sort? Ditto water company issues.
Then make a plan - 3 days of food/water/meds is standard, a week is better. Make sure your outside pipes have cladding/insulation on before the cold snap. Some blankets and hot water bottles are good to have handy if the heating packs up.
Look in camping shops now for deals on little camping stoves and a camping kettle. Always nice to be able to brew up something warm in a power cut. (Consider getting some hot chocolate & soup sachets in). (Obviously caution is needed if using this and preferably not inside!!)
Spare hats/gloves/coats so if you are outside playing in the snow and get wet and cold you can change. Some board games / cards / books to entertain everyone if it’s really coming down and you’re stuck in the house.
To get around the clear shelf panic buyers, consider having some UHT milk and part baked bread in (or learn how to make your own bread and get flour and yeast).
Meds are another important one - if you wake up with a rotten cold and the roads are shit, it’s nice to know you have some paracetamol / lemsip already on hand!! Some doctors/pharmacies will happily allow a slightly early prescription refill if there’s bad weather coming.
The main thing is prepare in plenty of time (as you’re doing!) not be day before the snow comes 