For the record, LV don't care about winter tyres. Back in 2010, I rang up and they charged me £35 or so (I got most of that back the following March). Come October 2011, when I called them up, they said that I didn't have to tell them and there would be no change to my premium as so many people were now putting winter tyres on their cars.
Contrast with Direct Line, who said they'd charge me £250, around 50% of my premium. Fortunately I was within the cooling-off period and was able to cancel.