I don't know if Satan actually changed their bodies, however Adam and Eve may have been "clothed in light" therefore not needing clothing. The opposite of immortality is mortality. So if God said that they would die or become mortal beings, then they must have been immortal. I've also read some interesting information on our blood which is our life-giving force, is actually a crystalized form of light. We had a forum author in the past who wrote about this.
Remember, God then forbade them to eat of "Tree of Life", otherwise they would be "trapped" in a corruptible body forever. The Tree of Life was how they maintained their immortality. So God allowed their deaths, covered their sins with "skins", and told Adam he would now have to wait for "the appointed seed", to redeem his immortality. That appointed seed would eventually be The Christ. "Jesus stated, that "no one puts new wine into old bottles, (or goatskins as some of the translations state). You put new wine into new bottles. " In other words, they would receive new bodies to replace their corruptible ones. That was the promise, and that is essentially the whole story of the Bible. From Genesis, "paradise and immortality lost", to Revelation, "paradise and immorality restored." and everything in between on how to get there.