ABS absolutely does help you stop on ice. Locking up on ice makes traction even worse; you get a miserable coefficient of dynamic friction and a film of liquid water instead of the already poor coefficient of approximately static friction you get while there's limited relative motion between the tire and the road.
It's not a panacea, but ABS definitely reduces the distance you slide compared to if you lock your tires.
Citation: Towed a trailer a few weeks ago in the snow, and even with my beloved Tekonsha P3 trailer brake controller it was a challenge keeping the trailer behind the truck while coming to a stop on curves. It's easy to test the effects of locking the tires on ice with an empty trailer trying to stop a coasting truck...the truck brakes, with ABS, do most of the work.
It's not a panacea, but ABS definitely reduces the distance you slide compared to if you lock your tires.
Citation: Towed a trailer a few weeks ago in the snow, and even with my beloved Tekonsha P3 trailer brake controller it was a challenge keeping the trailer behind the truck while coming to a stop on curves. It's easy to test the effects of locking the tires on ice with an empty trailer trying to stop a coasting truck...the truck brakes, with ABS, do most of the work.