Sorry for the late reply
I must start by apologising. Another forum I am on e-mails me when I'm needed, and I must admit that searching through the forum is time consuming. I am more than happy if anyone wants to send me a 'prod' giving me a clue as to which thread 'needs me'.
Back to topic.
Agree with much of what has been said.
1) If you don't have to - Don't.
2) Good tyres, well maintained, good pressures. Winter tyres a really good investment.
3) Treat gas & brake like they've got a raw egg on them - any big pressures and you're looking at a mess.
4) Plan, plan, plan. Look WELL ahead, use 'off gas' engine braking GENTLY (don't just suddenly take your foot off the gass). If driving auto then select the lower ratios before you need them otherwise the 'snatch as it goes down a gear may start a skid. If driving manual practice sustained changes . . .
Sustained change. When most people change down a gear they off gas, on cluthc, change gear, off clutch, on gas. In normal driving this seems to work well enough but there is a time when albeit momentarily the engine will be trying to make the wheels go more slowly (that was after all the idea of changing down) . In snow & ice however the wheels going more slowly than the car is a skid.
So, in good weather practice this - it does take some practice but is a really good technique to use at all times - it will lead to a smoother gear change.
Start by practicing this in 4th going to 3rd. Drive along a nice flat road at a speed that your car would hapilly go down a gear - let's say 40mph. Keep your right foot EXACTLY (and this is the hard bit) where it is. Now drop the clutch and the engine revs will go up - normally by around 500 - 600 rpm. It only revs itself if you have put more gas on - remember you MUST keep that right foot still. change gear, off the clutch and because the revs are already at 500 - 600 higher than you were in 4th you will find, somewhat magically that they are right for the new gear.
Go practice.
As an 'oldy' I can, and do - even on my modern car change gear, up & down without the clutch - YES it can be done NO it doesn't harm anything. If you can do this then you are already doing what amounts to a sustained change - you are getting the engine and gearbox speed matching the road speed.
Lastly and perversly - Be prepared to accelerate. If the car starts to move faster than the wheels - that's a skid. So if going downhill your choice of gear / gas is making the wheels go slower than the car you are in a skid. Recognise this and if needs be gently accelerate (despite all intuition) to get the wheels back up to road speed. In this situation brakes will not help - the car is already going too slowly for the road - brakes will just make it worse.