MINIs do quite well in the snow provided you drive prudently with the right set of tires. Your best bet for winter driving is to switch to a set of genuine winter tires (not "All-Season," although those are certainly better than "Performance") on 15 inch wheels. Many MINI owners buy a second set of wheels specifically for winter tires. Since MINI owners in warmer climates often like to upgrade their stock 15 inch wheels, eBay usually has several new sets of 15 inch MINI wheels listed at reasonable prices. MINI dealers also have wheel sets available. Mounting and remounting tires, especially runflats, can be laborious, but swapping wheels takes much less effort. Here are the current 15 inch MINI wheel part numbers:

36 11 1 512 458 (Silver 15 inch R81 7-hole)
36 11 1 512 347 (Silver 15 inch R82 8-spoke)

Don't forget the wheel caps if you need them. White wheels are available as well, but it's winter, and snow doesn't stay white to match your wheels, remember? Some owners like to run with steel (rather than alloy) wheels in the winter since they can be cheaper and since winter road salt slowly eats away all wheels. Generic 15 inch "steelies" might be cheaper, and MINI does offer official steel wheels (from the MINI One), but the 15 inch alloys via eBay are tough to beat, especially the cheaper and ever-dirty whites.

The 15 inch wheels (and tires) are the most effective in snow. They have "tall" sidewalls which better protect the wheels themselves in deep snow and slush. The MINI's original (OEM) tire size for these wheels is 175/65R15. These tires and wheels help "cut" through deep snow with their relatively narrow tread width. Other tire sizes, such as 185/65R15 and 195/60R15, may be perfectly acceptable. For more information on winter tire choices, please see the FAQ: What winter tires are available? Also check the Winter Wheel and Tire Gallery.

Check various dealers for the best prices. Here are some popular North American dealers:

Tirerack.com
1010tires.com
NTB

Note that none of the 15 inch tires mentioned are runflats so a spare is advised. Cooper S owners may wish to consider pricier runflats (195/55R16) and a set of 16 inch wheels. Studded tires are apparently not available in the MINI's exact factory tire sizes and such tires are illegal in some places. MINI dealers can order the official front snow chains if you need them for extreme winter driving conditions, but be careful to fit them correctly per your owner's manual.

Try not to run with winter tires past the winter weather season. You'll lose tread faster with each mile, so it's a good idea to get your summer tires on when there's a low probability of snow or ice. Also remember that winter tires are not an excuse to drive recklessly. Your driving technique will need to adjust in winter weather, and be especially cautious at the start of the winter driving season, when individuals cursed with vehicles other than MINIs forget how to drive to the conditions.

Some more tips: (1) If someone gets too near, or if the visibility deteriorates, turn your flashing hazard lights on. (Pull over to the nearest hotel or rest stop, well off the road, if conditions are bad.) (2) Try setting off in second gear if you're concerned about getting stuck in snow. (Check the owner's manual for advice about traction control if you have it.) (3) An extensive engine warmup is not normally needed in the winter -- follow your owner's manual for advice -- but be sure to get all the ice and snow off every window and every light before setting off. (4) Before opening the door to your MINI, wipe any loose snow off the top edge of the door to prevent it from falling on your chair. (5) As you step into your MINI, try first gently hitting your shoe on the outside edge of the lower door sill, step in with that first shoe, then do the same with your other foot. You'll keep the snow outside and your MINI neater. (6) If it's going to be below freezing temperature, some owners leave the hand brake disengaged (just it case it could get frozen in place). If you decide to adopt this practice, use wheel chocks or the equivalent (e.g. turn into a curb) if possible. (7) Consider carrying a folding shovel and small container of fine gravel (to toss under the drive wheels). These items might help you get out of a snowy situation. A warm blanket is a good idea, too, in case you don't. (8) Turn on your air conditioner about once a month, even during the winter. That keeps the seals in good shape.

There are a number of other OEM and aftermarket accessories you might find handy for winter driving. Some parts are only available via European MINI dealers (or North American resellers of European parts). If your MINI did not come with heated windscreen washer nozzles, for example, you may want to order the kit. (That seems to be the single most useful bit from the Cold Weather Package.) Headlight washers are also available (if you want) for halogen headlight MINIs. Rubber floor mats for the passenger compartment and/or boot can keep your MINI tidy. Front and rear mudflaps help keep your MINI's side and back windows clear, but you can't install them with the Aero Kit, and the rear flaps aren't compatible with the Cooper S. A kit to retrofit heated seats is also available for cold weather comfort, although most owners bring a short thermos of hot coffee to accomplish much the same. Rear fog light and extra brake light modifications make sense any time of the year. Here are some of the part numbers for these items:

61 66 0 029 716 (Heated Washer Nozzles)
61 61 0 029 748 (Headlight Washers)
82 16 0 136 806 (Front Mudflaps)
82 16 0 136 805 (Rear Mudflaps)
61 11 0 145 996 (Heated Seats)

Don't forget to pack your wireless phone and cold weather survival gear before you set off, and make sure your MINI is in tip-top operating condition with plenty of antifreeze washer fluid, including an extra plastic bottle. You do have a plastic ice scraper and snow brush, right? Be sure to read all the winter driving advice in your MINI owner's manual.

The front side of your MINI might be vulnerable to grit and stones thrown up by snow plows and trucks in the winter. You might consider a better skidplate to protect the underside of the engine compartment, such as the stainless steel version from Moss MINI. However, the skid plate won't help if the snow is too tall. (You will get stuck, so don't go diving into a snow bank unless you have someone along with whom you want to get stuck.) There are also protection options such as a front "bra" (usually made out of vinyl) or transparent plastic film, such as 3M Scotchcal thermoplastic urethane. These products are often generically called "chip guards" or "stone guards." Chip Guard Custom Designs makes a kit for the MINI if you want to install it yourself. Many MINI dealers offer similar kits with installation, such as the InvisiShield products listed on MINI's web site. MINI dealers also stock small paint bottles for color-matched chip repair, and many MINI owners recommend the similar but more easily administered (and more expensive) kits from Autovisuals. If you belong to a MINI car club this is one item you might be able to share.

MINIs are well protected against rust and corrosion thanks to a lot of modern manufacturing, although it is still advisable to wash your car carefully and frequently during the winter, with a nice coat of wax applied just before the winter driving season. Do not buy rust protection treatments such as Ziebart. At best they're a waste of money.

Window fogging, frosting, and grime are often big problems in the winter. In most countries, MINI dealers will fit replacement wiper blades under warranty at no charge. Many owners report good results with Rain-X window and mirror solution, with Rain-X washer fluid particularly convenient. Rain-X contains a "slick" polymer that helps keep windows clear. Don't forget to periodically treat exterior lights so that your headlamps and tail lamps will be more visible.