97 Passat GLX ABS light on

I put 20k miles on my 97 Passat GLX VR6 since I bought it as a used car. Now it has 72k miles on it.
Yesterday it was snowing in my city. I got shudder twice when I used the brake. I was told it is normal because ABS is working. Then when I tried to turn left to run up a not-so-sharp slope, my car kind of lost control in direction. I turned the steering very hard, and kept it to the end for about 1 minutes, before I finally got the control back and parked the car. At this time, I noticed both my brake and ABS lights were on. I restarted the car, and the brake light turned off, but the ABS keeps on.
I actually got ABS on for about 2-3 times before, but I was always able to turn it off by restarting the car. This time the restarting doesn't work.
I also got brake padal pulse sometimes, especially when I accelerate.
BTW, I may need to change my brake recently. But is it very related to my current problem?
I will send it to a garage. But can anybody give me a rough idea what the problem might be? Thanks a lot.