Continental's Top Contact II Winter Premium tyres are the answer to general very cold weather riding in the UK. Note the 700x37mm version measures only about 31mm wide; yes, the fronds sticking put may add a few more mm, but if they brush mudguards or anything else they add very little resistance and wear off anyway - so the '37mm' version will actually work with any bike with clearance for 32mm tyres. The 700x42mm version measures a true 42mm wide. Continental really ought to produce a true 37mm version, and a 28mm version wouldn't go amiss either.
I find them excellent, and use them in most frosty/icy conditions unless the ice is severe and extensive, in which case I deploy Schwalbe Marathon Winter studded tyres - i.e. I use the Top Contact Winters frequently on ice as I typically find it on the southern UK road/lane/path network (including countless miles on ungritted lanes) - thick hoar frost, rime, frozen rain, frozen run-off etc are all fine with caution on these Continental tyres.
Studded tyres are horrendously slow though, and on a 15-mile commute will probably add around 15 minutes' riding time over something like a Continental Gatorskin or Schwalbe Durano, whereas the Top Contact Winter will probably only add 7-8 minutes for the same riding effort. Studded tyres inspire a confidence even on extensive sheet ice (although caution is still required) - studs are lethal when cornering on road ironwork, though, whereas the Top Contact Winters are fine on dry metal and generally fine on wet metal with caution.
I quite happily ride across icy patches on the non-studded Top Contact Winters - yes I do need to exercise caution, and take extra care to corner more slowly than normal, but they cope admirably and riding a straight line across ice on them is very straightforward compared with non-winter compound/tread tyres.
For muddy and wet leaf road conditions, I use the Continental Top Contact II regular tyres in various widths depending on application, which have a fairly aggressive tread but still roll reasonably well due to a smooth centre strip. Definitely noticeably faster than the Top Contact Winter. The 700x28/32/37/42mm versions of these tyres are all fairly true to size in terms of tyre width.
Successful winter riding is all about the right tyre choice (and clothes) for the conditions. The only conditions that will stop me are deep snow and winds above about 70mph.