A Warforged isn't actually "living armor," though. A Warforged in 3.5E has composite plating, which provides a +2 bonus to AC, which can't stack with anything other than natural armor. This armor could be different based on their construction (by taking a feat at first level), having the composite plating be adamantine, mithral, or unarmored body (allowing the Warforged to wear armor like other PCs). This implies that the Warforged are the living construct beneath the armor, made of wood, metal, and other things, and that the armor itself is something attached to the body.
The 4E warforged function a little differently. Under the Physical Qualities header of the warforged (4E Eberron Player's Guide, p. 33), it says:
Warforged are bulky humanoids covered in plates of metal and stone. A skeleton of these materials supports woody fiber bundles that comprise a warforged's muscular system. Warforged bodies have an internal network of tubes filled with a bloodlike fluid that nourishes and lubricates their systems.
A warforged can modify its body, adding and removing limbs as necessary. A warforged feels pain only from real injury. These physical modifications allow warforged to vary in appearance as much as any other humanoids.
Also, in the equipment section of the Eberron Player's Guide, under Warforged Components (4E Eberron Player's Guide, p. 113), it says:
Warforged can use items just like other races, yet as living constructs, warforged can also utilize items specifically designed or enchanted for them. A warforged component often grants a special advantage to a warforged. Warforged components are not worn or carried; instead, they are either attached or embedded in a warforged. Like normal items, warforged components have categories, such as armor, weapons, implements, clothing, rings, and wondrous items, and they occupy a warforged's item slots.
So 4E warforged can wear armor. They don't have any natural AC bonuses. They can wear regular armor if you like, or, if you'd prefer, you can have the armor attached to your warforged's body, making it impossible to remove while you are conscious.
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