Brake Issue with a 1995 Pontiac Grand Am?

I have a 1995 Pontiac Grand Am with the 3.1 V6. I am having an issue diagnosing the issue that i am having with the brakes. There will be times when i am turning into a parking spot or coming to a slow stop when i will get a whirring sound from the brakes when they are applied. It sounds as if the anti lock brake system is trying to engage, but is not fully performing its duty since it will lock the brakes in one place instead of applying them multiple times to keep from locking up the tires If it is dry outside or slightly wet with rain i do not have an issue with the tires other than its a slightly uncontrolled stop...and a bit of annoyance. But It will lock the tires when it is snowing or icy on the roads, which for me is not a good thing. I have not had too much of an issue with it, since i know its going to happen so i compensate for it, but i would like to be able to resolve the issue, so that i could confidently allow others to drive my vehicle. If anyone could offer me some suggestions to look at or a definite answer that would be fantastic. There are not many places around here that i trust not to rip me off and none of them offer a free estimate.|||wheel speed sensors bad..the ABS lite is on right? i pulled the fuse on mine because i got tired of paying 150 dollars a sensor...after 2 no more ..No ABS, no problem.