Why 1st or 2nd - why not 3rd or 4th?

In the days of automatics with 3-speeds plus overdrive 4th, the "Winter" programme would usually start in 3rd.

In slippery conditions you won't be getting very much torque/power down on to the road anyway.

Most modern turbodiesels with manual gearboxes are easy to get rolling from a standing start in the snow: simply releasing the clutch gently in first gear will raise the rpm slightly without having to touch the throttle (the cars' ECUs have a routine built in to protect the DMFs, activated by a switch on the clutch pedal).

You can do the same in most petrol cars if you're smooth with the clutch.

I often do that, even in the dry, particularly in stop-start traffic. Even with my 1.0l petrol (no turbo) it has more than enough torque without using the right foot.

I wonder whether pulling away in 2nd gear was more useful with older cars, particularly when they're running a bit rough in the cold weather?

My Mazda3's first gear is very fierce - despite it being only a 1.6 petrol engine, it wants to race away at the slightest increase in throttle in that gear, so I find that I get far better (usable) traction in very slippery conditions when I move off in 2nd gear (with very little difference in clutch take up than using 1st in normal conditions). You should always use the highest gear practically possible (without needing to slip the clutch all the time) in snowy conditions for this reason, changing up early as well.

Don't forget that the frictional resistance between the tyres and the snowy/icy road surface is considerably reduced, meaning that it requires less torque to get the wheel moving, and too much (in lower gears or driving normally) would easily cause wheel spin.

Traction control is useless in such conditions as well, which is why I don't have much issues in this sort of weather, as my car is a Euro-spec car (RHD) without traction or stability control - never needed either in these conditions, even with both sets of summer tyres I've used on the car.

snowy conditions for this reason, changing up early as well.

This is another thing I'm not sure about. If I for example, do 15-20mph in 2nd gear, I can easily reduce (or increase) the speed gently. In 3rd gear I can't really go much slower without the car trying it push forward. With snowy icy conditions the traffic speeds tend to vary a lot, so by changing up early I spend a lot more time changing gear (and taking a hand off the wheel) and braking.

Of course, it could be that the recently conditions haven't actually been that slippery. If it was really bad then I wouldn't be doing 20mph.

I think it varies from car to car, especially as regards its engine torque and gear ratios. Mine are geared more for performance, your may be less so. For example, 15mph in first gear in mine is past the 'smooth' change to second - more like me giving it a LOT of right foot. I normally, in good conditions (not pushing it), change from 1st to 2nd at around 10-12 mph, 2nd to 3rd around 20-25mph (it can do 15 in 3rd if on the flat, but it'll labour if going uphill), and 3rd to 4th around 35-40mph. The gearing seems short in my car for smooth driving, but you get used to it.

I used to work in a Saab dealership where various staff members (apart from us lowly valeters!) would get to go to Sweden on a winter driving course where they would be shown how to drive on ice and in deep snow. I'm not 100% sure about this but i think this is where i heard about starting off in a high gear, from one of the samesman after i witnessed him driving his girlfriends car out of a car park (on a hill) in 3rd gear without any wheelspin. She had tried about 5 times to get it out herself in 1st. I have also used this method myself a couple of times where it was impossible to get moving in 1st as there is simply too much leverage on the tyres regardless of how gentle you are being with the throttle. I certainly wouldn't use this method readily due to the obvious potential for knackering the clutch, but, in my experience, it does have its uses.

I did try snow mode on my second car which was fine until I encounter a speed hump going uphill! In the end I had to roll back, turn off snow made and get a slight run at it.

Moving off in second came about as the early four speed boes were based on three speeders so that first was more of an emergency low!