isn't it to do with surface area and spreading the weight of the car over this area?
Wider tyres spread the weight of the car over a larger area and therefore increases the chances of the car "floating" over the snow rather than cutting through it to the road surface.
If the tyres are narrow the weight of the car is spread over a smaller surface area and thus the tyres have a better chance of cutting through the snow.
I didn't to GCSE physics so I could be talking out of my bum. If someone could throw up some kind of official sounding theory that would be great.
To some degree, yes...you are correct.
However, it's more about compound and tread pattern.
Would a 225 wide tyre be worse on snow than a 165 wide tyre? Probably...given the tread pattern and compound were the same.
Would a 225 wide winter tyre be worse on snow than a 165 wide slick tyre? Unlikely.
If you want to fit winter tyres - or skinny tyres - just for in the snow...than fine...but you could also fit chains.
however, most of us want the ability to drive their cars normally when it's not snowy...and I'd like to see the insurance company pay up if I binned my Mk6 GTI on 165 wide tyres.
Fitting the standard sixed tyre but in a winter compound does not affect the insurance, means I can use it in the snow, and still go the top speed in Europe with correctly speed rated tyres.
Comparing narrower tyres with wider tyres...there will be a difference, if you go to extremes.
But my father uses 205/50/16 winter tyres on 6.5" wide wheels his Mk5 GT170 TDI and I use 225/40/18 winter tyres on 8.0" wide wheels...and there is NO obvious difference in the cars abilities....
Make of that what you will.