Tyre tech time - grab a seat and a cup of tea, it's about to get crazy....
Most tyres contain a limited amount of natural rubber, the compound that makes tyres 'rubbery' (strangely enough!). As a cost saving exercise, manufacturers replace natural rubber with man-made (synthesised) rubber - the cheaper the tyre, the more cheap synthetic rubbish (hence why they're called ditch-finders, they last forever but have no grip whatsoever!), the more expensive the tyre, the more natural compounds, although still only in a relatively low percentage as manufacturers are always judged on tyre longevity, and nice soft supple rubber doesn't last long! Super soft vs medium compound anyone?
So basically, a 'standard' tyre isn't going to be fantastic in low temperature - tyresafe.org suggests 7c or below, but it's more like 3c and below - as the synthetic rubber hardens.
A great real life example of this is - have you ever noticed how on very cold mornings, if you get up to 50mph plus within the first 1/2 mile or so, it sometimes feels like there's a bit of steering vibration, like wheel misalignment? You have to pay attention, but it's there. This is the tyre solidifying in the cold, creating a small flat spot that goes once the tyre warms up.
So in theory, a tyre with more natural rubber will have a lower operating temperature than an average road tyre. Of course, tread pattern and all the other fascinating elements of tyre production play a massive part in cold weather performance, which is why an R888 in soft compound might still not be your ultimate winter tyre!
One of the major factors in winter specific (or snow) tyres is that they contain significantly more natural rubber than a standard tyre. You can physically feel the difference if you dig your thumbnail into one, especially if compared to a standard tyre. They also have more tread (between 8 and 13mm, depending on the tyre), and are covered in sipes (slits in the tread blocks) that allow the tread to move, generate heat, grasp snow and flex to uneven surfaces. Because of the increased movement, they do have more sideways roll which takes some getting used to, but is great fun and very predictable! A decent winter tyre will work well for you in all winter conditions, only losing out to a standard tyre when grip comes back out to play.
So what does all this mean for the OP? Basically, I'd suggest you invest in either a premium set of all weather tyres just for winter use, or go whole hog and get a proper set of winter tyres on steelies or cheap alloys and know that your Westfield will go out and play, whatever the weather! I'd avoid the likes of R1Rs, T1R's etc as they are more dry weather focused (not saying they're not good in the cold/wet, just comparing to a tyre designed for the purpose). And do bear in mind that ALL tyres suffer the releasing agent issue, so some patience is required on any new tyre. Or, accept the reasons for low performance of standard tyres in winter and expect the slidey-slides!
If you've survived this far, I apologise for the useless information I've just downloaded on you, but now you have an insight into my nerdy brain!