This is how the game was played when it was first released, believe it or not. We didn't get an enemy health bar until the first patch.
Anyway, you can try this mod: http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=7317
Hmm, it seems like it should be possible. I'm no expert with the console, but im sure there's gotta be a way. On the xbox version of morrowind there's a glitch that makes it so you don't see the enemies health bars if you hurt them with magic, but that's it. So if it's on the xbox version as a glitch, im sure either a console command or a tweaking of the Ini file should be sufficient enough to take away the health bar.
Worst case, im sure somebody out there made a small mod that disables health bars somewhere. I mean, somebody else must have thought of it before.