My car's brakes don't work in the snow?

The car is a 1998 Ford mustang. I believe it has antilock brakes. I was driving in the snow today, (it rarely snows here) and when I tried to stop, the brake pedal went straight to the floor but had a vibrating feel and slight grinding sound to it. The brakes didn't stop the car at all. Luckily, no cars were in front of me. When I got onto a clear road, the brakes worked just fine. Why does this happen?
Added (1). The pedal felt like it had no pressure in the snow. The pulsing/vibrating was from the pedal, not the actual brakes.

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