Well I’ve got pretty new all season good tires but I think we are expecting ABS to do more than it really does. We just had snow yesterday and there are several intersections that are pretty well polished. With ABS fully activated, the car still slid a little side ways. All ABS is supposed to do is rapidly brake a wheel and release it so in theory the wheels don’t slide. In actual practice though on ice, it just can’t totally prevent tire slippage. And there is nothing wrong with my brakes or ABS. That’s just the way it is with cars. Plus the same thing will happen in reverse on the traction control when trying to start up on ice. You have to let up on the gas a little or the car will pull to one side. That’s why as much as everyone thinks ABS is so great, sometimes you can do better by just manually applying the brakes for the conditions.
In other words, those tires were probably not much good in the first place and now they are even worse in low traction conditions. Best would be to replace the tires.