Bob - are winter tyres worth it? Very definitely!! I fit them every Nov. and leave them on till the end of March.
Just had winter wheels and tyres fitted to the AMG C43. Michelin Pilot Alpine rubber. The worst part was that to fit them I had to buy a set of alloy wheels to fit over the massive brakes. The result, whilst eye-wateringly expensive, is that the car now feels glued to the road.
I've considered winter tyres for the Plus 8, but again 4 new alloy wheels needed to clear the discs and calipers, so for the milage I drive in winter a bit indulgent.
As to washing the underside, I don't.