I'm sure others more expert than I will weigh in here, but if you have anti-lock brakes they shoudln't make things worse. In fact, the usual advice is to maintain steady pressure on the anti-lock brakes (don't let up), and look in the direction you want to go. This saved me from crashing into someone's mailbox on a winter night a couple of years ago, and it's what I was taught more recently at an AARP driving class.

Also, I learned recently that older cars will continue to give the engine gas even after you take your foot off the accelerator, BUT most newer cars will not. This is one of the gas-saving features of newer cars. I noticed my new (to me) Subaru slows dramatically when I remove my foot from the gas pedal, unless I'm going downhill. It took me a while to get used to this. Putting the transmission in neutral couldn't possibly make it slow down any more than it does in drive.

Maybe I'm wrong, but I'm thinking there are risks involved in putting your car in neutral. For one thing, you lose the ability to get out of an unexpected bad situation in a hurry.

Manual, yes.
Not a good idea for an automatic transmission.

"our automatic transmission drivetrain was engineered to be left in drive while the engine is running and the car is at a state of rest at lights, and elsewhere.

However, your transmission was not designed to be shifted between drive and neutral an extra however many times (thousands? tens of thousands?) over it's lifetime by people who don't leave the car in drive.

Your engine is fully capable of stress. At a red light, in drive, it is idling probably at 700 or so RPM's. It is relatively unstressed. There is very little load on it.

However, every time you shift a transmission into drive, you are jolting the drivetran (transmission, axles, mounts, etc). As well as actuating the mechanisms that shift it into drive in the transmission. Constant shifting back and forth will cause undue stress and wear on all sorts of components not designed for those repeated stresses.

So leave it in drive. Your engine is well up to the task of handing it!"

Here is a link that might be useful: 1 link of many via Google

If you are sliding on icy roads, the correct response is to take your foot off the accelerator, keep your foot OFF the brake pedal, steer in the direction of the skid and look in the direction you want to go.

Tried and true advice from professional drivers that I have followed for almost 40 years of foul weather driving.

I just asked my husband and he said "when you are driving all four wheels are working to slow you down when needed. When you hit the brakes two are working but, when you put it in neutral none are working and you're putting yourself at risk as you have no way to control the car. He thinks it's a dangerous method to use. My son is a race car driver. I'm going to run it by him next time I see him. He said the car is not meant to be moving when it's in neutral.

"you put it in neutral none are working"
The brakes work in neutral.

Yes, the brakes work in neutral, but if you need immediate power to correct the skid, you're SOL if you're in neutral.

I was taught to drive by two generations of racecar drivers and they'd laugh their heads off at this "advice" to shift into neutral. Modern automatics are "smart."

Leave the car in gear. Sheesh.

They also recommend doing that if your accelerator ever sticks and you can't slow down (as the news as covered those horror stories before). You can still use your brakes but it disconnects the engine from the wheels.

Putting your car in neutral while driving it, is very hard on the transmission, and can lead to a very expensive repair, besides being a very dangerous thing to do. It takes control away from the driver, and could cause a serious accident.

My brother learned years ago that putting your (automatic transmission) car in neutral while driving is a Very Bad Idea (tm)

He borrowed the extra car without asking to visit friends, and was returning home late and wanted to avoid waking the parents and have them know he took the car. So he decided to pop the car in neutral, and quietly coast to a stop along the curb in front of the house. When he put it in neutral the car made a quick little crunchy/grind-y noise and gave a little shake, and rolled onward to where he wanted to park. However the next time someone tried to drive it and needed to go in reverse, reverse didn't work at all.

I'm sure that he went a little too far past 'N' and reached 'R' and the crunch and shake was the reverse gear being destroyed. The funny part is that our younger brother who inherited that car after we left for college, continued to drive it without reverse for the remaining years he was at home and even for the entire time he was in college.

My Dad used to tell me "pump the brakes" on ice. But it never worked because I'm really scared and instinct tells me to push the brake pedal down hard and slow. My current car has anti-lock brakes so I think this is best for me.

the only good thing I learned to do when we lived in wa state (and all these hills!) was to come to a complete stop before making a left turn! here in flat mi, it's not so bad!

If you have anti-lock brakes (ABS), do not pump the brakes. Apply steady pressure to the brakes. You will feel the brakes pulse.This is normal. Pumping them overrides their
technology.