What cold weather tyres do you recommend for driving in Europe?

I need to take my Jag XF AWD once each year to Luxembourg during October. Do I need cold climate tyres and if so which do you recommend? Priorities are comfort and legal.

Can I mix different tyre brands front and back on a 4x4?

I have a 2011 BMW X1 xDrive on run flats. I don’t mind the harsh ride but they are Pirelli P7 and seem to lack grip in winter. It has 255/40 R18 95V on the back and 225/45 R18 91V front. I expect to need...