I've only read the first few responses so lots has probably been said already. But here's my thoughts...
Yes get a freezer - doesn't need to be a chest one, just a decent capacity one. Always have a bottle of milk and loaf of bread in there at least, and some frozen veg and a couple of days of meat or dinners (ready meals or dinners you have made yourself and frozen whether batch cooked or just leftovers) for any emergency. Might be snow, or a flood, or a blockage on the road, or just run out of petrol or life gets frantic and can't get to shops for a few days longer than expected.
Build up a decent storecupboard. This is a combination of:
- things you always use anyway, just making sure you always have a spare to spread out trips to town (the extra bag of rice or pasta, tin of tomatoes, box of cereal, packet of biscuits).
- ingredients to make meals easier when life gets hectic or plans fall apart in some way - a couple of jars of tomato sauce or curry sauce, tub of custard and tin of fruit to put dessert on the table, tub of hot chocolate powder to cheer up DCs while they wait for a meal, part-baked bread (usually lasts at least a couple of months in packaging)...
- baking and other basic supplies - the ability to bake bread and cakes, manage when power is out, cope (and even cheer people up) in bad weather are all important. So tins of beans or spaghetti that can be heated in a pot, tins or packets of soup, a tub of powdered milk, or tins of evaporated milk, mini marshmallows for the hot chocolate, etc. Ingredients to make meals from scratch gives you a better range of options - for example, fajita seasoning from a big tub is used in our house to make fajitas, but also Mexican type stirfries over rice (fry veg, meat, season, add tinned tomatoes, maybe natural yoghurt), season BBQ ribs, added to ommllettes (sp?), and add interest to potatoes thrown into the oven to roast - all completely different meals.
- some foods that don't need cooking - tins of tuna and sweetcorn to make tuna sandwiches (or melts if you have the grill), crackers and cheese....
- emergency supplies: bottled water, couple of tins that are meals in themselves (the beans, ravioli, decent soup).
just think these things through and build up your supplies over time.
Always have milk, cheese, butter, something to put on bread (jam, ham, Nutella...), tea, coffee, etc in the house. And toilet rolls.
I run my shopping list so that people mark up when items are running low, and I get those as needed. And have a big check of the pantry and fridge and freezer a couple of times a year (one always in early autumn before winter and Christmas buying commences).
Try to plan your shopping so that you always have at least a few days food left in the house before you go shopping, not down to the last items. And you may need to change how you shop if you are used to popping into a local store to grab dinner for that night - whereas now you need to buy most of what you need probably weekly at most (we used to drive 25 miles to the city every weekend but most around us used the more expensive convenience stores and occasionally got to the larger town 10 miles away).
Look for things that you can buy and freeze on shopping day to use later in the week/fortnight/between shopping trips, especially meat and fish. It's also useful to have a couple of ready meals and treats there too - maybe hit up a large Sainsburys/Waitrose/M&S occasionally and get a large bag of things to eat over the next couple of months rather than having a takeaway. (You might find that planning to have a coolbox/freezer bag and some iceblocks frozen to bring on those larger trips useful, especially if you already own anything for picnics etc).
Yes, find a good supplier of oil and make sure the tank is not empty. You will also need to get used to checking that occasionally to see if you need to order more.
Maybe get the boiler serviced if you don't know when that was done last.
Get all chimneys swept too if you don't know that previous owner had them done recently.
Find your wood supplier too and also make sure that it will be stored somewhere dry.
And that you have the tools for the fire (metal tongs, metal scoop/pan for emptying out, and a metal bucket to put the ashes into).
New house means new emergency escape routes need to be thought of for everyone to get out anyway. Think about it, tell the DCs, and be happy they know what to do. (This goes for any new house regardless of location - but may need more thought in rural areas as to "where to go to phone fire brigade" or "where is a safe place to go to if I can't find mum or dad" type questions).
While thinking, also think about what rooms are colder, where is wind getting in or what might need extra insulation. Do you need to draught-proof some doors and windows? Would putting interlining in some curtains help (blanket-type lining to help keep heat in the house)?
Are all the radiators working right, or is there air in some that needs to be bleeded out? Is the heating system sufficient to heat the house? Would some extra throws in some rooms be useful to snuggle under, or extra blankets/electric blankets/hot water bottles be needed on beds? Would heavier clothes be a good idea, or extra layers (not always meaning thermals etc, but things like always wearing socks rather than bare feet, or a cosy hoodie or cardigan to throw over the everyday clothes in the evenings at home)?
And are there any damp issues? How are you going to deal with laundry - is there a dry place outdoors to hang it (covered space), or a line for dry days, is there a tumble dryer, or do you need to use clothes horses indoors? (And will this cause any other issues)?
Having some candles or nightlights, matches, and a safe place to leave them while lighting, is important. If the neighbours say electricity outages are common, you might want to have some other lighting like solar-charged lamps (camping lights could work ok), oil lamps (paraffin lamps, tilly lamps etc) somewhere that you would all spend time together in and would be bright enough to do homework by in winter, or maybe even a generator. But you should probably also think about having a torch in everyone's bedside locker and in the kitchen, to be able to get around.
A couple of powerbanks, normally kept charged up, could also be useful in cases where the power goes out - especially for mobile phones.
And a drawer for batteries that you always replace! (Or rechargeable batteries that are recharged as soon as power is restored!).
Entertainment for when power is out is also useful - books, musical instruments, pack of cards, board games etc.
And an alternative form of cooking. Do you have only electric or can you get gas? Do you have any camping gear that you might have even a 1 ring stove (to use outdoors) - now could be a good time to get any end-of-season items that could be useful? Does the wood-burning stove have a flat top that you can put a kettle or pot on top to heat up even if slowly (tin of beans/soup can be heated this way, or even a stew done slowly all day)?
And while you only need a couple of bottles of water permanently, (Tesco bottles are cheap and perfectly sufficient once sealed for years), having some kind of containers to fill if you do have a water outage (planned or not) would be good - you might get a chance to fill them before it goes, or water may be restored at night to allow tanks to fill, or you may have to fill from a tanker or well outside the house at some point. Again, camping supplies might be useful, but even keeping an empty 5l bottle from a supermarket, or having a couple of large pots or clean buckets could do it.
Have proper winter clothes - rain gear, wellies, hats/scarves/gloves etc. So that you can all get out regardless of weather. Whether that's just for a walk, or there is a blockage from snow and you need to get to neighbours/bigger road.
Get to know the neighbours to learn about the local customs, suppliers, what is normal or not, etc. If there is no local village, there might be a meat supplier who comes monthly to everyone, or a farmer who sells veg direct to the public, that could be good to know, or there may still be a milkman doing a round. Do people join together for any items, like fuel (oil, wood) deliveries, or infrequent large purchases like buying a lamb/pig/cow between them already butchered for the freezer? Or do they have a barter system - Mary makes great jam in the summer, John does tasty home brew every few months, Sophia makes delicious crusty bread once a month on baking day, your garden has a great herb patch that the previous owners used to share out... Or even just know where is good for foraging, or good shops that are local but not direct, (so don't head straight towards the town, but go left at X point and a mile down that road is a great small store which always has A and B items for in between shopping trips, or shop Y 2 miles the other direction always has fresh milk and stays open late, but shop Z only 1 mile away is usually out of milk and closes early). And knowing the local professionals - Dr, dentist, vet, hairdresser, barber, beautician, chemist,.....or whatever else - who may operate out of rooms in individual houses or be mobile rather than in the town so far away. Where is the local library and bookshop, or a good place for occasional AmDram or musical performance (even if not a proper theatre or cinema, there can still be lots of culture), or sports clubs or hobby groups.