The X body was a completely new design at GM. The first few years were like prototype cars- nothing like them had been built before, so several weak spots were revealed which were later improved upon by GM.
This is the X body hallmark weakness. Most X cars (and 86 and previous A cars, J cars, and N cars, as well as the front wheel drive C cars and H cars) will experience this sometime during the car's lifetime. When starting the car cold, particularly in the winter, you may find that the power steering is unusually stiff- it feels like you are driving a car without power steering. After a few seconds or so, the power steering returns to normal.
What happens is that the aluminum interior of the power steering rack has become scored, and the teflon seals in the rack no longer fit well. As I understand it, this prevents the flow control valve inside the rack from operating properly, causing the steering to not have power assist until the car warms up a little.
For every car, the situation is different. It may just be a minor nuisance in the morning that never gets any worse. You always will get power assist back after a half minute or so. In other cases it gets worse quickly. If you don't get power assist and the car has warmed up, you need to get the rack replaced.
There is no real "quick fix", although I've heard adding 10W-30 motor oil can help for a little while. I don't know if there are any negative side effects of doing this, however. Changing the power steering fluid will prolong the life of the rack even if the scoring has already begun to happen (because there are metal filings in the fluid from the aluminum rubbing off inside the rack). If it isn't too bad, you're best off not worrying about it.
If you get a leak in the power steering system, either get it fixed or keep the level topped off, because the rack will wear if it is low on fluid and create this condition in a perfectly good rack. Lubrication isn't sufficient when the fluid level is low. If you ignore the fluid level you will feel the steering wheel shudder as you turn it or that it binds at one point as you make a turn. If it has gotten this bad you need to replace the rack.
The real solution is to replace the rack with one that has steel sleeves in it, to prevent the scoring inside it which causes the problem. If you have a shop do it for you, it could cost $350-$500! If you do it yourself, the rack costs about $120, but it is a pain getting the old one out and a new one in. A really good idea would be to go to a local technical college where they teach automotive courses, and wait for a steering and suspension class where they can replace the rack without the labor cost.
Happily, these are generally cheap and easy to replace. Front wheel drive cars are hard on their motor mounts because they prevent the twisting motion of the engine on turns and on acceleration. The rubber in the mount either tends to get crushed or it dries out and shrinks. If you hear a clunk when accelerating from a dead stop, check the rubber out inside of this mount. The three mounts between the engine/transmission and the K frame wear out much less frequently. The rubber inside them can also dry and shrink, however. If your transmission shifts roughly into drive or reverse, check these mounts. This is much more likely to be a problem on an 80-82 model than an 83-85 model. These are really easy to replace and only cost about $25-$30. Get a good one that will last a long time when you replace it. In newer cars, the mounts have been improved. This is a lesson GM definitely learned from these cars.