I have wood blinds on my steel door. I don't think this is a problem.
Use a fresh drill bit designed for steel to predrill your holes. Buy an extra bit or two. I think I broke one, maybe two doing this.

Kathymichigan, thanks that will help. Did you use sheet metal screws? Or regular screws?

Yep...use sheet metal or self tapping screws. But if you use a 1X2 board you will need a very long screw. Better to use a 1X1. You can also screw small "L" brackets to the door first and rest the board onto the the brackets and screw the bracket to the board.

I just clear caulked the magnetic brackets onto the doors. You have to pay attention for a few minutes - to push them back into place if they slip, but it doesn't take long for them to hold. Mine have been up for two years now and are still going strong. HTH.