Not trying to beat a dead horse or be a dick or anything, but how do you know that the wheels are locking up? Is it because you are losing control? Ice or any type of snow will do that to your car when you are on your stockers. ABS won't slow you down. It is only really designed to give you control in situations like this. But if you don't have control, then I would just assume that the snow/ice is too much for the stocks. That crunching you feel, is it pushing back at your foot? If it is, then it's your abs working. If your abs light isn't on or if it stays on for a longer than normal period of time during start up, then you have a problem.
Bottom line, my best guess is it's because you are still on stocks and are driving in ice and snow. But if you still feel that it's not, then by all means take the car in. Not a good idea to drive around with brakes, or lack of.
Good luck.