Hire a 4WD with winter tyres.
There's no point buying a set of winter tyres and having to pay for them to be fitted and then pay more for your normal tyres to be put back.
That is a crazy suggestion really. Just had a look on Enterprise at small SUV rentals. Now, baring in mind the OP didn't say how long he was going for, so I just picked a week long rental in their smallest SUV, and for one with an auto box (which you would), was £360 for a RAV 4 (goes up to £420 for an XC60).
Now, again, I don't know what size wheels the OP has on his BMW, but, assuming 17's like my old man has on his e90, so 225/45/17 and 255/40/17, a full set of Vredstein Wintrac Xtremes come in at £389. So a little more than the cost of a weeks hire of the Rav 4, and a little less than the XC60. But either way, much safer overall due to actually being made for the conditions.
Sure, there may be a cost to fitting the tyres. £40 or so. But that isn't a huge amount extra to pay. The OP could buy a set of second hand wheels cheap enough for it so he only pays it once, and has winter wheels for the next 4-5 years.
There is a set of "square" wheels, so same 225/45 front and back, on ebay for £160 just now, even with what looks like useable summer tyres, which could bring back half that cost. The wheels would always be worth £80 or so without tyres, and brings the cost of the winter rubber down to £340. So £500 all in (well, minus delivery and fitting) for wheels with new winter tyres, which would likely be worth £400 anyway after a weeks use, so £100 for the safety factor for a week, rather than ~£400 for a weeks 4x4 rental, which will inevitably come on summer tyres. Plus potentially £80-100 worth of summer tyres.
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