Bloody hell 
I am totally confused now. Went down to the local tyre centre, where the chap has always been brilliant with my tyre choices etc.
He stated that I do not need to change my wheels, that he can get me a decent set of winter tyres in my size and that they will be more than adequate.
God help us I don't know what to do now.
Giz
He is correct. you don't need to change them.
But 225 wide tyres are crap in snow regardless of the compound...far better to have a narrower tyre, but you can't get that on a 18" wheel.
225/40/18 winter tyres are fine in the cold, as that's the size I run...but I'd not want to drive in deep snow on them.
In snow, you are likely to slide and more likely to clunk a kerb. The hifgher sidewall of a 205/55/16 gives you more protection from damage - to both the wheel and tyre, and the car's suspension geometry.
Monza Shaddows in winter, with gritters throwing stuff about = white worm by spring.
It's a no brainer to me...if you NEED to drive in really bad weather, you need to give yourself the best possible chance of finding grip, with the least chance of damage to the wheels/car should a slide occur.
So cheap winter wheels with 205/55/16 tyres is THE best option.
17" or 18" winter tyres are far better than 17"/18"/19" summer tyres...but nowhere near as good as 205/55/16 winter tyres in the snow.
Only you can decide how important the journey is, and how much you are prepared to put at risk.
Poll