Is eczema considered an open wound?

Yes: When in the midst of a flare-up eczematous skin can certainly be considered an open wound.

Depends on situation: If the skin is just thickened & rough but maintains a good barrier, it can be seen as closed. If it has open weeping or oozing areas it is open & susceptible to bacterial infection.

Not usually: If the area is or has been bleeding, I would call it open. Usually from scratching. If no bleeding has occurred, would not call it open.