Dropouts are solid steel. Usually they're painted, although paint scratches off here with clamping the wheels on. Stainless dropouts are a good idea but relatively new in implementation; many older steel bikes have chromed dropouts, which are very nice as well.
However, despite paint scuffing and subsequent possibility of surface rust on dropouts, they're completely safe. If frames ever do rust out, it's from inside the tubing, which is narrow and a good environment to keep moisture. The dropouts are thick steel, and on the outside of the bike where they dry quickly.