For wet conditions, I know that the wider the tyre is, the higher the actual grip level, but the lower the aquaplanning threshold.
But for snow?
Well, the studded snow tyres that the WRC cars use on the winter stages are noticeably narrower and higher in profile than tarmac tyres, but I can't confirm whether the same principle applies for road tyres.
In any case, if the majority of your mileage is done on summer tyres, then high quality 17 inch winter tyres and rims may be more cost effective anyway (and provide more traction I suspect, but again I'm just guessing).