Do a search for prices on mytyres, camskill etc. You can have them fitted to existing rims, or purchase new steel wheels for them to be fitted to. This may be a better option so you can get narrower rims, but check with BMW which size will fit.

No you don't need to sell it, your RWD car will go anywhere any car will once you put some suitable tyres on it.

BMW offer winter tyre services now to their customers, probably your first point of call to get a ball park figure, they'll change them over and store them for you too.

You have several options depending on whether you have runflats and wish to stay on them...if you do it will restrict you options drastically.

Assuming you are prepared to get or indeed already have a spacesaver spare or are going to buy a tub of goo and inflator pump, i wouldn't get goo/inflator but many seem to manage, these are some of the options.

1. Spare set of wheels, could be new steel wheels with winter tyres already fitted, or you could find a set of used suitable alloys on ebay or similar and get winter tyres fitted.

You could get slightly smaller wheels probably and go narrower with higher profile, the purists say narrower do the job better, and i wouldn't argue with that, however you need expert advice as to what will fit and any deviation from standard size is a mod and the insurance could clobber you.

For what it's worth I run wide full winter spec low profiles on my RWB benz and they are absolutely fine, i had even wider full winters on my pick up, they were even better, you do not need to go different sizes.

2. Keep to your own one set of wheels and get a handy little chap to swap the tyres over twice a year.

3. Replace the existing set of tyres with proper winter rated (snowflake symbol stamped) all season tyres, not quite as good as the best winter only but run a very close second. They excel in cold wet weather, whcih is 90% of a Britsh winter.

This would be my choice unless i was keeping the car for 4 or 5 years to get the use from a set of purpose winter tyres. Several good quality tyres fill this gap, Goodyear Vector, Kleber Quadraxer, Vredestein Quatrac3, in no particular order...there are others of all budgets but make sure they have the snowflake stamped on the sidewall, can be (deliberately?) confusing on some sites.

It helps with a RWD to have a couple of sandbags at home ready to chuck in the boot if severe snow is imminent whatever your tyre choice.

Costs wise, option 3 is the cheapest as they are straight replacements, some people will tell you that all seasons wear badly in summer, this could not be further from the truth in my experience with Vred Quatracs and from a good source Kleber Quadraxers wear well too.

Whatever you decide don't hang about, once the weather starts turning cold the prices will go back up and there'll be another shortage.

Some people suggest fitting winters to the drive wheels only, i would not do this, you end up able to get drive grip but still have summer slicks doing your steering and most of the braking.

its well known that BMWs are not the best cars to own in wintery conditions, but thats only because people who own them dont know how to use them in the winter when it snows,

winter tyres can help anycar (unless its a 2cv then thats just silly) gain traction in the snow, i would advise to get some steel wheels just for the winter because there is nothing worse than scratching your alloys from skidding a little bit