Smear a little wax or grease over exposed metal (except braking surfaces!!) to stop further corrosion.
Rust on the exposed pedal spindle is fairly common and harmless.
Grease can pick up dirt so I prefer car-wax.

I used to live by the sea and ride the seafront every night, even during storms. The steel-framed bike was exposed to a lot of spray as well as rain and never came indoors for 2 years.