Squealing power steering belt

When I bought the car (18 months ago) supposedly all fluids were flushed and all belts were replaced. It was bought as a used car with about 70,000 miles on it and the dealer did a good job of going over just about everything on the car. At that time while replacing all the belts the power steering system was flushed and checked out. I tend to agree, although just about everything "other" then replacing the pump was done, it looks to me like the pump is failing. I also put a wrench on the pump pulley to rotate the pump and I thought it was interesting that the pulley AND belt turned somewhat easily with the belt rotating without slipping at all on the pump pulley and I could see that the belt was slipping easily around the engine pulley. Of course there were mechanical geometry things in play with the torque of the smaller pump pulley being applied to the larger engine pulley. But I would have thought it would have been more difficult to turn. In short, when turning the pulley by hand the belt slips only around the motor pulley and doesn't slip at all on the pump pulley. So all things considered, my thought is the pump is seizing when cold and after it warms up in 60 to 90 seconds it frees up. Just weird that it works perfectly all summer and the problem only shows up when it gets to an average temp. Of around 45 F. Or lower which kept me thinking it was a "belt" issue.