Yes, snow and ice do reduce friction. Really, no $hit? But no, that doesn't really repeal Newton's laws of motion, does it? And, why would putting it into reverse stop you any faster, if you cause flashover, and are still sliding, with less surface area on an iced rail, offering less even less friction.

I'll use the air, and keep generating as much friction heating as possible from the much larger surface area of the brake shoes against the wheels, which is why I'd use sand, and even a little power to keep the wheels turning and slowing the momentum by converting it into heat energy, and not allow it to begin to "slide", ice and snow or no ice and snow. Because that putting it into reverse will stop it faster "in the snow" is utter nonsense.

No, I've never switched on ice, I ran on the LA Division. But, I have switched on a track well greased with plenty of corn oil at Wesson Oil, and I did just fine with properly using the air brakes, in just the manner I described. And, since I took physics, I'm going to go with the science, over this "old head" yarn about putting into reverse..