How can I stop white, salt-like powder from appearing on the block walls of our basement cold room?

The white build-up you see are a mineral deposits called efflorescence. It happens when small, invisible movements of liquid water migrate through the basement masonry, bringing with it dissolved minerals. As this water reaches the inside surface of the blocks it evaporates, leaving minerals behind. As the process of inflow, evaporation and mineral deposition continues, it creates the fluffy deposits you see. Muriatic acid quickly dissolves the minerals, but to stop more from appearing you need to block the movement of water. This was the idea behind the recommendation to paint the wall, but ordinary paint is no match for determined water. You need something specially made to prevent water movement through masonry, and I know from experience that Drylok and Xypex both work well. There may be other good products out there, but I’ve never used them. The only hitch is that both Drylok and Xypex need to be applied to bare masonry. You must remove all paint before application.