When you're in sneak mode, just fire an arrow at a door. The enemy will investigate it and go through the door.

I normally fire an arrow to get the guy in a better position for my next arrow.

Does this work with all doors?

Little off the topic of "enemies through doors." but I myself (before 1.9) once found a location (I believe it was in the palace in either Solitude or Windhelm) where I could walk into the doorframe, go through the door (which was a travel port) and be outside the room, then fall into the floor beneath me. Found it by accident when a guard or someone opened the door and pushed me through the wall (I believe i was sneaking)