1993 Other Oldsmobile Models Steering Rack or Pump Problem

Usually its the rack when it happens cold, also it seems to be the rack because you are hearing the wine which tells me the pump is working. Replace the rack

Mastertechtim is right, but I had this problem too in one of my cars, and to my surprise, I needed a front end allignment, let me explain. The turn ratio was way off causing my car to make a whine like your describing. When they alligned it correctly the whining ceased. The rack had to move farther back and forth than normal causing it to whine. What I'm saying is give it a try, you may be able to get a lot more time out of your rack before having to change it out