Interesting discussion this, and nice to see that people in UK are talking about this ("at long last" IMO). All the best to those who've already taken the plunge, and hopefully, the following may help waiverers to decide in favour.
The general situation here in Switzerland may help with decisions, where, when I first permanently moved here in 1990, I'd never heard of winter tyres, apart from the studded version which I'd only experienced on hire cars in Scandinavia (studded tyres are banned here BTW).
It may be that the situation here is a bit different to UK generally speaking, but contrary to popular belief, not all of Switzerland is mountainous. For example, I live "in der niederungen", i.e. it's quite low down here (400M ASL), and although hilly (often, say about 20% or so gradients), in a normal year we won't normally get more than 6 inches of snow at any one time down here. And "down here in the flat lands" we don't have an army of snow ploughs just standing by either - for example, our village of roughly 1,500 people has one snow plough (a Unimog with an attachment).
Although the "major" roads in/out of the village (bus routes, etc) are ploughed and gritted almost immediately after a fall, and thereafter as required, they'll only get around to the rest of the village such as my (residential) road a day or so after a snow fall. Generally the roads are often quite narrow, some corners are quite tight, and as said, it's often quite hilly. In general I'd describe our area as being somewhat like small villages and smaller towns in Devon or the Lake District.
A "normal" winter here will see lowest overnight temps of around -10 deg C, (we did have -17 C for a few days one year) and day time summer highest temps are typically in the mid/high 30s C (though this year we touched 41 deg C for a few days).
Winter tyres are standard here and are normally fitted once the ambient temperatures
regularly comes down to about 6 or 7 degrees C. They are then replaced with summer tyres once the temps regularly get up above that again (and with the snow all gone of course). In a typical year that means a change to winter tyres sometime in October or perhaps November (due to the very hot summer and long India summer this year past though, we changed ours in December). And change back is normally about late March/early April, again temperature dependant, and once the snow is all gone of course.
BTW winter tyres are NOT legally required here, but if you do have an accident, even if you can prove it's not your fault, you will have a HUGE problem getting your insurance to pay out. That's in contrast with Germany where within the last few years winter tyres have become a legal requirement, though I'm not sure exactly what the change trigger point is. I'm also not sure about the situation in France although where I live we're only about 20 mins drive from the borders to both those countries (nearest points). I'm also not sure about the legalities in Austria (about 2 hours drive from here).
The main point about the winter tyres is that the grip is FAR above what is normal for summer tyres, even on loose or hard packed snow/ice. HOWEVER you do not drive like you're fireproof and can plough through snow banks, blizzards, or ignore the normal rules about no sharp acceleration, braking, and steering! You can't do those things with impunity, but if you do get into a skid it's normally only mild, and easy to control.
But what you can do is reckon that with winter tyres, getting up and down pretty steep snow covered hills and round sharp corners you'll have much more grip than you'd ever get with summer tyres. So if you get caught on roads before the snow ploughs have been out; if you're crossing lanes on the Autobahn where the snow ploughs have left frozen ridges; or you're in a car park or driving where melted snow has run across cambered roads and then refrozen at night; then you're MUCH better off and safer than with summer tyres.
On my car (a bog standard Peugeot 308 automatic) I have a set of 4 x Michelin Alpin Green, and my wife's 207 manual has similar (I'm not going out to the garage to look). Both cars are front wheel drive; mine a 6 speed auto, hers a 5 speed manual.
Having never owned or driven an automatic while in UK I should perhaps say what the Peugeot auto box is like, in case UK spec cars vary.
Apart from the normal "P", "R", and "N" settings, the normal setting is "D", when the box just does it's own thing and changes up and down all by itself. There are also 2 secondary settings for the "D" position, "S" for "sport" (when the box holds each gear to a higher rpm than normal before changing up), and "*" which is the snow/ice setting where the box moves up through the gears as soon as you get moving, getting to 6th as soon as it "thinks" it's OK. In winter with snow and ice I normally drive in "D*", otherwise just in the "D" setting. The box also allows manual changing where, just like a manual box, it will stay in whatever gear you select until you change up or down again. But it's very seldom that I use that facility, except up in "the real mountains".
Lots of winter tyres are available and you can specify whatever you wish (there's a large range freely available), but we just normally let the garage fit whatever they recommend. For our cars they cost the equivalent of about 180 quid each here, and fitting a set of 4, including balancing, will cost about 80 quid equivalent. The normal "deal" when buying a new car is to negotiate with the dealer for a set of 4 spare wheels with a set of winter tyres already fitted (steel wheels usually, especially if the summer tyres are on ali wheels) - it's a further "discount discussion point" on the overall car price!
You can either store the 4 extra wheels/tyres at home and change them yourself twice a year; or more often, as in our case, the garage stores the unused wheels/tyres for you (for a nominal charge) and you book an appointment when you want to change over.
As well as being much better than summer tyres on snow and ice, winter tyres also offer much more grip in the wet, and on muddy roads, etc, so in practice they stay fitted for 4 to 5 months per year. Typical life for us is about 4 seasons (say 50 to 70,000 Km), with summer tyres perhaps doing about 5 seasons (say 100,000 Km). Normally we need to change tyres in pairs, rather than sets of 4 at a time (front wheel drive cars remember).
But if winter tyres are so good, why change to summer tyres at all?
Well I'm not a tyre expert but we are TOLD that the winter rubber compound is softer (maybe, how do you tell?) and on winter tyres you can certainly see the tread pattern does look different. So they SAY that if fitted all year round winter tyres would wear out much more quickly. Personally I don't really know that for certain, never tried it, I just do as everyone else does ("when in Rome" and all that).
BTW, in contrast to a post above, our winter tyres are noticeably noisier than summer tyres - not hugely so, but during the first few Km after change you certainly do notice the increased noise level, regardless of the road surface (or reduced noise when back to summer tyres).
Unlike up to about 10 years ago (when you had to paste a special speed limit sticker on your speedo - "slower" winter tyres were a bit cheaper) there are no speed restrictions on winter tyres now. And tyre pressure settings are the same, summer and winter.
But overall, having been forced (once only!) to try and drive a car with summer tyres up the snow covered hill to our house (sharp curve half way up and about a 15% gradient) and having been unable, even driving backwards (rear wheel drive car) I'm now convinced that winter tyres, used sensibly, are the bull dogs whatsits. I'm also convinced that if winter tyres were the norm in UK then you would not see the miles of stopped traffic on the motorways to and from Dover (just an example) that we see on the TV news here every time there's been more than an inch or so of snow!
As another bit of info, the mountain passes here all have big traffic signals advising if the pass is open or closed, (sometimes closed) or only open if driving with chains (mandatory to fit before starting and mandatory to remove once through - there are special laybys for the purpose). I would have thought it wouldn't have been too expensive to apply something similar to things like the trans-Pennine roads in UK.
All the above applies to light commercial and service vehicles here too (vans, minibuses, ambulances, etc). I'm not sure what the rules are for HGVs and not being a biker I have no idea what goes on with them, although the number of powerful motorbikes seen on the roads in winter here is noticeably reduced (I think people just garage them over winter - we have a system here where you can take a vehicle off the road for a period and consequently pay less road tax and insurance).
Anyway I hope the above is interesting and helps UK drivers a bit. A few years ago when UK had a particularly bad winter I remember the then Minister of Transport (can't remember the name but I think it was in the Con/Lib coalition government time) saying on Radio 4 that winter tyres are not generally appropriate for UK. Either plain ignorance or just disingenuous (IMO only of course, but based on the above practical experience)