I was told that using rock salt on hay that is kept in a small area would keep it from molding. Is this true, and would it do anything to the hay other than keep it dry? 

The basic answer is yes, salt (sodium chloride) can be effective in inhibiting growth of mold organisms in hay. In earlier days, the practice was not uncommon for small rectangular bales. After stacking a layer of bales, usually with the "cut" edge facing up, salt was broadcast over the surface before proceeding to the next layer.

Salting was sometimes done on only the topmost layer or two of the entire stack. This is where mold is most likely because bales normally undergo a process called "sweating" in which a slight temperature elevation evaporates excess moisture. This warm, moistened air moves upward through the stack. Some of this excess moisture tends to condense on the upper bales because air outside the stack is cooler.

The problem is that surface broadcast salt was not terribly effective. It could not be distributed thoroughly throughout the bales. More effective preservative materials are available today that accomplish the same objective by spraying solutions, usually containing ammonium propionate, during the baling process for hay above 20% moisture at baling. Ammonium propionate effectively inhibits mold growth and does not appear to be toxic to either horses or cattle. Good ventilation during storage is also important so that any moisture that does leave the stack is eliminated as quickly as possible