I completely agree with desertstorm's posting above! First, when the weather has turned bad, it is probably too late to organise getting some wheels and winter tyres, maybe slightly easier to get winter tyres in winter nowadays, but in the recent past once the allocation had been sold, or the demand has dropped off, the excess tend to migrate back to where the bigger demand is in mainland Europe. Second, the present trend over the past maybe 20 years has been for "normal" tyres fitted to new cars delivered into UK to be Summer tyres, which has in the past been okayish - but these tyres have been evolved into "summer only" tyres, the place that I buy Michelin tyres from, has for a few years now, always warned people about considering using these summer tyres in winter conditions in Northern Britain. Finally, the current trend is for local authorities to get their budgets cut back, so road snow clearing and gritting is a bit slower/later or not at all in places, which can mess your travel plans a bit unless you have tyres that work okay in ice/snow - and the obvious benefit in really wet conditions.
One thing to consider, even if you have four wheel drive, the chances are that with "summer only" tyres in nasty winter conditions, you will get moving okay, but steering and braking will become a bit of a lottery, which is not good for you or anyone around you!
Edit:- If I'm being completely honest, initially when I bought my wife a new Polo with 195/50 X 15 alloys in late 2002, things seemed to be okayish, she is a safe driver but choses to use back roads to get to work as a teacher - so if she does not get to work and the school is "open" then no pay. Changed the Dunlop Sports for Michelin Exalto Pilots when they were worn out, okayish for a couple of years then she started to complain about grip in winter, so I bought a set of steels with 185/? X 14 Alpins and that made a lot of difference to her commute. Meanwhile I just kept going with my four wheel drive Passat with its Michelin Prem***** summer tyres - until one year I could not safely drive back down my driveway! So as I had the original factory alloys lying in the garage, I set to getting myself a set of Alpins for my car - in December, none new in UK, so I managed to buy a very slightly used set via ebay, they made a lot of difference to how my four wheel drive Passat, and I've kept on using winter wheels/tyres for six months a year since then.
Some people say that fitting winter tyres is very dangerous as you will go out looking for trouble - that only works if you are an idiot.