Had tough time getting paint to stick to even the cleaned surfaces of trailer. As several some have said, Ospho is not a paint -- it's a metal cleaner or treatment. (Several posts seem confusing.)
If you "paint" with
Ospho, rust will come back because the surface is not actually painted. It is just prepped for the paint.
After you strip the rust off, the surface has to be coated again. There is a
cold galvanizing spray if you have minor touch-ups. Also Krylon makes what they call a cold galvanizing primer.
It's hard as heck to get paint to stick to zinc galvanizing if even little bits are left on the metal. You've got to clean and "etch" the surface in order to get the paint to bond.
I used an inexpensive wire cup brush in a drill and buffed the small rust areas, then used cold galvanizing spray. No Ospho. If you've got a massive amount of rust, then what J and others said about blasting is prob better.