I've just had an issue with Skyrim that google didn't know the answer to. One of my NPCs - Rumarin from interesting NPCs - had an invisible body. Usually, this issue is due to an armour mesh being broken, so the solution would be to reinstall any armour mods and verify the game files in Steam. That wasn't the problem I had. Rumarin was invisible in both the thieves armour, which showed fine for other characters, and in no armour.
The problem I had, it turned out, was that somehow, the NPC had been set to "invisible race." The fix was to open the console (tilde key,~, below the esc key), highlight the NPC - either click on them or type "prid <ref ID>" - then type "setrace <race>", in this case, "HighElf."