If its slippry, like ice slippery, it won't make much difference. If you are stuck in snow then you want to leave air out to get more rubber on the ground and have a bigger foot-print and more traction. At normal speed though, don't mess with the tire pressure.
Had a pair of all season radials on a car that when the temperature dropped in the low 30's they got slippery in wet conditions. I needed 2 more tires and when I went back to the tire dealer I said I wanted something different because of this problem. He was baffled because I was the first person to complain about these tires and for the 20+ years in the tire business these were one of the few he was actually excited about.
I chalked it up to the compound of the tire and temp but at his advice I upped the tire pressure from 32psi to 35psi and it was a night and day difference. Going down in pressure sometimes isn't the way to go.
Generally, all you have to do is open your driver's side door and look at the little sticker. Ya might need a magnifying glass for this. It will tell you The tire size that is supposed to be on your car. It also tells you the tire pressure that you are supposed to have in said tires.
Now it gets tricky........If it's only you in the car....Go with the recommended tire pressure.
If the significant other is with you, 2 more pounds in the passenger side. If she is fat, 4 more. (Gotta keep it level)
Now, In case of snow, what you really need is a few of her friends.....If you put enough weight in the poor car, it will go. It'll be wheezing and farting, but it will go with enough weight in it.
No reason to adjust the tire pressure, just adjust the unsprung weight....till it won't move.
In all honesty though, The tire manufacturers in this day and age have a good handle on what their product will do. Just keep them at the correct pressure and you should be good to go.
Nope...wasn't ice....it was tire pressure.
Vehicle manufactures reccomended tire pressure and tire manufacturers reccomended pressures are totally different.
My experience resulted in better traction and actually made a slight improvement in gas milage.