It happened to me before. Not in my Impala, but in my old car (Civic) one winter I drove it into a ditch or pothole or something in the middle of the road that was about wheel height. It wasn't dry snow either, it was that wet slush. Naturally I got stuck, so after much pushing, pulling, screaming, cussing and flinging slush everywhere, I finally got out. My ABS light came on and the car felt like it had a slipping transmission, probably the ABS unit cutting power to the wheels. Turned out I had soaked my ABS sensor, and after a day or two when it had dried off, everything went back to normal.
Now, I'm obviously not saying this is definitely what is happening to you, but I definitely agree with @sheila
and I think you just got your sensor and / or their associated wiring wet. How long ago was this? If it's been a few days (of sun) and you think the sensor should have dried out by now and the issue is still on going, then maybe try to pull an ABS code? Do note, you'll need an ABS code reader to pull an ABS code. Most common, cheaper OBDII code readers can't pull ABS codes.
Please do update us! Hope this helps some!