If you’re cleaning a pane of frosted glass, then you’ll have similar challenges to clear glass.  By design, the surface of a pane of frosted glass isn’t smooth – it’s covered in tiny imperfections which diffuse the light passing through the window.
It does however all depend on the type of frosted glass you have. The effect is achieved either by etching with acid or blasting the glass with sand at factory level, or with the help of a special spray-on frosting. The former variety can be cleaned in the same way as a pane of ordinary glass. The latter is vulnerable to wear over time, and will need to be periodically refreshed. Do this with the help of a roll of masking tape, which will protect the rest of the door.