A little web searching will turn up lots of generic, top ten lists of things to do to winterize your car. Most are just common sense; not all apply to Minis; and what you do will vary depending upon whether you are going to store the car for a few months, or if your Mini, like my daily driver, lives outside all the time.
All the list builders seem to think that checking tire pressures would be a good idea. Well, duh! You should be doing that more than once a year anyway. Pretty much the same goes for checking all belts and hoses and changing the oil and filter. As a conscientious owner of an older car, you are already doing this type of maintenance year round, I hope.
A more practical suggestion would be to check the coolant mixture. Even though you are not expecting very cold weather, error a little on the safe side and try to end up about 10 degrees below what you think you’ll need, and don’t forget to take into consideration that planned ski trip. How do you know how well you are protected? You can get coolant testers at any half-way decent auto parts store. The real cheap ones (floating ball hydrometer types) can be as low as a couple of bucks. For a little more money a better quality hydrometer (floating needle) can be found. That’s what I use. If you are looking for high end types, refractometers can run you $50 and up. (They can test battery fluid, too.)
Another important item to check on Minis is how well the wiper and windscreen washer systems are working. At best, Minis are marginal in both areas. I bet a good look at your wiper blades will have you ordering a new set. And a test of the washer system (after you have topped up the fluid) will probably have you looking for a small piece of wire to dig the wax out of the squirter holes.
Another marginal system is the windscreen defroster. There is not much you can do here, but do check to make sure the blower is working and that the hoses from the blower motor under the dash are connected. It doesn’t hurt to seal them with some tape. There are products on the market that are supposed to help keep the inside of the windows from steaming up (hard to do in a small car!), but I haven’t tried any of them so I can’t advise. At a minimum, throw a small, clean towel in the door pocket.
Add a battery check to the list of good things to do. A marginal battery can get you through warmer weather without giving you a clue it’s not up to snuff. That drop in temperature into the 30s may surprise you with a car that is reluctant to start. Make sure the cables are clean, and locate the engine to body ground strap in the engine compartment to make sure the connections at both ends are clean. Check the water level in the battery cells (if you don’t have a sealed battery) and test the fluid “potency” using a cheap, hydrometer type tester (another item to pick up at the auto parts store).
If your car is going to sit for some time during the winter, the rules change a bit and you need to look at things like fuel stabilizers and maybe even a battery trickle charger. Car storage can turn into a big topic, so I encourage you to do some web searching if that’s what’s in store for your Mini.