Basically what the title says--I noticed the Unicorn horn causes the Unicorn to get a "coat" of glow, and there was a mod to remove the vampire glow, but it's outdated.

Any and all help is appreciated

Twallan's Debugenabler can remove the shine of the vampires, and since that mod can remove many other effects maybe it can do the unicorn too
http://nraas.wikispaces.com/DebugEnabler

I never knew! Which option? How does it remove the vamp shine, please?
And can it remove the glow on genies, too?

I don't remember it very clearly but if you click on the vampire sim (with debug enabler) there is an option called "visual Override". Clicking that gives you something like vampire and Heat Vision. Then just hit the remove visual override. Your vampire sims turns normal, though his/her profile picture (avatar) still remains with that effect
I tried this once but since it (or any other vamp mod I ever used) does not remove the glow from the avatar, I stopped using debug enabler. But you could give it a try, maybe it can remove other occults' glowing effects too
Of course Twallan would know this better

A-HA!!! I noticed that visual override thing but didn't know what it did, so I left it alone. But I'll try it out now; thanks!

Cool An Thanks
But unicorns are the only occult, who is not included.
Is there another way, the glowing of their body to get away?

Removing (or adding) a visual override with DebugEnabler is very unreliable anyway, because it will only hold over a game session. As soon as you save and reload the override will be back (or gone again, in case you added one).