Is it ok to screw into a steel door?
It's definitely not a problem.  As @ChrisF mentioned, the best way is to drill a small pilot hole (1/8" would probably be about right) and use a self-tapping screw.  

"Self tapping screws" suggest that you don't need a pilot hole, but they're really meant for sheet metal.  They'll never get started in the steel skin of your door.  A small hole will let them engage.

Drilling steel is not like drilling wood.  Please forgive me if this is too basic, but someone else might find it useful.  

To drill the hole, first locate where you want it with a pencil.  Then use a center punch with a hammer to tap a small indent right where you want the hole.  If you don't have a center punch use a nail.  If you don't tap a center mark, your drill will skate right across the surface of the door and scratch the paint.  

Then drill at the full speed applying some pressure directly behind the drill motor, in line with the twist drill.(1)  If you're used to drilling wood you might be surprised how much pressure it takes.



(1) A bit (ha ha) of anal-retentive vocabulary: the thing that you plug in is the "drill motor".  The thing that actually drills, which most people call the "bit", is not a bit, it's a drill, usually a "twist drill".  I only bring this up because the the anonymity of the interwebs makes me bold.