http://en.wikipedia.org/wiki/Obsidian#Current_use, swords were made from that (the look like maces to me but still).
Obsidian turns green from some imperfections (metal).
Besides they practically say it's just steel armor with glass on it to distribute the blow.
If it was steel armor, wouldn't it fall under heavy? With Oblivion's design, it looks like it consists of chainmail with glass on it (at least the exposed metal parts look like chainmail.) so I could imagine it might be made from steel, which I would presume is also what Oblivion's chainmail is made out of (or it could be iron, I suppose.), but Morrowind's glass armor looks more like solid plates to me, and it seems to have much more metal parts than in Oblivion. I don't think it could be light if it used steel.
Also, at least according to the UESP article on it,
Glass armor is a lightweight armor created using rare metals studded with volcanic glass. The result is stronger than steel due to its ability to absorb and distribute shocks very well.
, I'm not sure what these "rare metals" might be, but steel seems pretty common in the Elder Scrolls.
In any case, though, obsidian is probably the closest real world equivalent to glass as used in glass weapons and armor in the Elder Scrolls, though given that they don't call it Obsidian and it always appears in a green color, whereas real obsidian tends to be pretty dark if pure, in the Elder Scrolls, glass doesn't even seem all that dark, although it is brighter in Oblivion than in Morrowind.