I never understood how to use automatic transmission in snowy/icy conditions. To me it's basically a lottery. With manual transmission and clutch I can actually recover from a slide almost immediately (the moment you start sliding you disengage transmission right away with clutch and do initial correcting maneuver which you cut short the moment you feel any kind of traction in order not to oversteer; it takes some practice on each car but you can try it on empty parking lots during winter nights). This is not possible with automatic transmission, the neutral gear still drags wheels, driving them to slide. Of course, if you have a 300+hp engine and are a race driver, you might try to correct it using full throttle, but don't try that with a normal car unless you want to massively increase your chance of hitting traffic.
Let off the gas and steer where you want to go . . . it really is that simple. Letting off the accelerator is more-or-less equivalent to pushing in the clutch. I've never (well, hardly ever) had trouble recovering from a slide in an automatic, and I've never really practiced it except by accident. Anyway, if you are sliding regularly in snowy/icy conditions, you might be driving too aggressively or you might just need snow tires.
> I never understood how to use automatic transmission in snowy/icy conditions. ... it takes some practice
The second part of your statement I quoted above is how. Recovering is identical except for the declutching (instead, if it is a power generated skid the reaction should be to reduce power). But the true part of the recovery (be it with a manual or automatic tranny) is performing the correct wheel turn in the correct direction and amount to recover. And getting that down requires enough practice so that the reaction becomes muscle memory habitual. Once that is done, recovery in an automatic is just as trivial.
You'd be amazed how many people, who never had any training and have never practiced skid recovery, have the initial reaction of turning the wheel the wrong direction (hint: almost everyone who has not ever practiced the maneuver will do this) - which of course simply makes the skid worse.
Automatics have traction control. The computer that operates the traction control is much faster at taking power from the wheels than a human using a clutch.
Apply throttle, point wheel, let whatever the manufacturer brands their dynamic control do it's thing. I grew up driving a manual on northern New England backroads in show and ice, and I'm quite proficient at it. My 328 wagon is far, far, better than me. This shouldn't be surprising, as it has a much higher-dimensional control space to work with, and much finer grained sensor data coming in.
Many Americans live outside of your area. Anyone who has experienced rain in California knows that people don't know how to drive in the rain. But it's not just there. You see people driving just as close to cars in front, without headlights or sometimes using high beams, unable to demist their windscreens etc.
Is "steer into the slide" the same thing as the above comment to "steer where you want to go"? I literally don't know what steering into the slide means. If my front end is sliding right and my back end is sliding left then I should steer which way?
If you're on an icy road (or other low traction surface like oiled stone or gravel) and your car starts pointing/moving/spinning to the left, you want to turn left to keep the front wheels moving and regain control and dump as much speed as possible without locking the wheels. Don't touch the brakes until you have traction!
That's counter-intuitive for many people as typically you want to actually go right.
If you have a manual transmission and you know what you're doing, in some situations you can downshift and use the engine to slow you down more. But in my experience, it's a "nice to have" vs a must for passenger vehicles. (different story for big trucks)
"Steer into the slide" means if your car is rotating clockwise you steer left such that you reduce the friction on the front end (by turning the wheels so they roll instead of slide) and maintain the friction on the back end (given the wheels will not be pointing forward).
(edit: depending on how far you've already rotated, but I'm speaking as if the front of the car is still ahead of the back of the car)
If you have a capable system an automatic can be an advantage.
My car has several modes including Sand and Snow. Both modes will remap the transmission and provide more/less torque. In some modes it will even start in 2 so you don't spin your wheels and get stuck. The throttle response in the pedal will also be increase/decreased as well as the sensitivity of the steering wheel.
You can avoid skidding on the corners by going a little slower? I drove an automatic Camry a while in a ski resort and the only real problem was when the gradient got too steep so you couldn't get enough grip to get up which is not a transmission problem.