Would you down shift a car with an automatic transmission on slippery roads?

Probably not.

It would lend to instability. If a front wheel drive is involved, the experts say to accelerate to maintain stability. This is a no win situation as you get going faster than the road conditions allow.

If it is a rear wheel drive, the easiest thing to do is to let off the accelerator and coast to a slower speed. this is the natural way to regain control. I believe the reason most front wheel drive cars end up in the ditch when it gets slippery is because of the former. If the road is slippery and you drive automatics then you may have better control if you use a higher gear so the wheels do not spin as easy.