I don’t, but my mate put winter tyres on his Cayenne and they are 275/45 20 load rated so you should be able to find a suitable tyre.
While it’s a 4x4 it’s still a heavy beast (2.5+ Tonnes) and it certainly stops well in the snow and Ice. So I don’t think you have to go skinnier for winters.
However....
What I found was that the bigger winter tyres get seriously expensive. So worth looking at how they cost out compared with say 17 inch winters and a set of 2nd hand alloys. Also you need to factor in the cost of getting the tyres swapped as the seasons change.
Personally I reckon the second set of Wheels is the way forward, as it normally works out cheaper over a couple of years.