I grew up on a farm which was 5 miles from the nearest village shop and it is 20 miles to the nearest town with "proper" shops like Boots, Lidl etc.
When it snowed, we could be snowed in for days, so I gained a siege mentality from my mother when it comes to food supplies 
.
I still live in the area, but on the edge of the village with the shop, but even then, in bad weather, the milk and bread supplies vanish at the first mention of a snowflake. Only the main roads are gritted, so the supermarket vans can't deliver to most houses.
So top tips:
Candles - real and fake with plenty of batteries
Power banks - keep fully charged in winter months so that you can top up your phone.
Milk and bread in freezer
and a plentiful supply of Pasta, Soup, baked beans, spaghetti hoops,
Cheese and crackers,
I have a 2 ring gas stove and spare gas canister, so I can at least boil water/heat up the above mentioned foods.
We have oil heating, so if the elec goes, no heat, so we have plenty of fleecy blankets and warm jumpers.
I was actually better off when I lived at the farm because they had to power the generator 24/7 to be able to milk the cows and keep the milk tank working, so always had elec no matter what the weather was.
Be prepared for the schools to close at the first sign of a snowflake, as all the children will have to be bussed home again safely.
Our nearest cinemas, museums, big supermarkets, shops etc are all 20 miles away, so I buy most things online now. The nearest McD's or Pizza Hut or Costa, all 20 miles away.
Taxis are also miles away, Uber's don't exist. The nearest city is 2 hours away, as are eating places like Nandos, F&B, TGIF etc
Stock up on wood, firelighters, kindling, matches, batteries. Get battery operated candles for the DC to take to bed if they can't sleep in the dark
Keep an old plug in corded phone, so you can keep in touch with the outside world if the power goes.
Order heating oil in the summer not the winter, as it is cheaper usually and don't run out in winter when it snows like my neighbours did, as you won't be able to get a delivery then.....
Buy a sledge in the summer because you won't be able to get one for love nor money when snow is threatened.
Don't drive on steep ungritted roads, there is one local notorious hill that most people end up turning their cars over on!
But you know, country life can be great, it is obviously very different to city/town life and it is just what you are used to/get used to when you live there.