The three common possibilities are: (they are not always all offered on
any specific door model or by a specific manufacturer).
They're actually not quite hidden at all! If you look VERY closely at many of the photos, you will notice that the main door frame piece across the bottom is a fraction of an inch UP from where the side rails go. If that was 1/4" high, by 32" wide, that's 8 square inches of available opening, PLENTY for the air for a fire! (The SECRET of the hidden damper has been exposed!!!)
JDoor's
Fireplace Door Selector Page is at:
http://mb-soft.com/juca/info/doors/firedoor.html