Righty tighty.. Lefty loosey..

Actually ... it depends on what you're fastening it to.   You won't like it, if you put a screw through the outer skin of the trailer.  If you're asking about screws to a frame member, make sure you know what's behind the surface.  Wiring doesn't take screws or drills well.  There is always adhesive too.

Post some more details for a better answer.

Thanks for the reminder about watching out for the electric wires - hadn't thought about that!!

What I want to do is hang a peg hook rack and one of those pocket organizers on the trailer door, hang a curtain rod above the window, and a coat rack in the corner...

If you can, check at your nearby hardware store and get a few lengths of flat steel that have numerous holes along the length of it. Have them cut it to the length you need. Attach THAT to any frame sections inside the trailer (tack/ dressing room area I suppose?)- then you can more easily bolt, clip, clamp other stuff to it.  If you are putting stuff up in the horse area, make sure the edges of the steel are ground or filed smooth, or cover it with that rubberized tool handle goop, so it doesn't injure a horse.

Screwing into your trailer door. It depends on your door's construction. If it looks like it's "paneled" (with steel/alum), you'll have a hard time if you try screwing at the very edges where the frame is. Try going in a few inches.  Drill a pilot hole first.  

I have found that magnets are WONDERful for hanging curtains ... : ) I got some clippy-magnet kind.  I'll probably replace them with more traditional curtain rods as I work on insulating and finishing the dressing room of the GN.  Get the big monster ceramic magnets from the hardware store.