I know you Brits don't do winter tyres, but that's what I would recommend. Both the Pirellis you've got now and the Michelin PS4S are high performance summer tyres that doesn't really like the cold and wet weather.
A set of high performance Pirelli or Michelin winter tyres will perform better through the cold winter months.
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F10 520d M-Sport Alpine White | HRE P43SC 20x9+20x11 | Michelin PSS 255/35+295/30 | KW V3 Coilover | M5 Front Sway Bar + M550d Rear Sway Bar | 3DDesign Front Lip | BMW M Performance CF Spoiler | BMW M Performance Diffuser | BMW M Performance Black Grills | BMW M Performance Pedals |
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