The main source of horror marks is certain items. Don't give any of these items to your pretender. Problem solved!
Oh, wait ... you can also get horror-marked by a handful of spells (or a very rare magic item) in combat. Okay, so don't take your pretender into combat. Honestly, a pretender who stays in the lab -- researching/forging/casting -- will not get a horror mark unless you equip a Very Evil item.
However, you might want to take your pretender into combat. Fair enough. Demigods on the battlefield can be pretty cool. Actually, combat isn't very dangerous when it comes to horror marks. As stated earlier, horror marks in combat are only inflicted by a couple of rare spells and magical items. Frankly, taking your pretender into combat is much more likely to get a curse, an affliction, or just-plain-dead. To further minimize the chances of getting horror-marked, choose your opponents carefully.
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Summary: Yes, getting horror-marked is No Fun. However, it's also very avoidable.
Learn what causes horror marks, then avoid those things. Once you get the hang of it, your pretender will be safe from those nasty horrors!
Of course, other bad things can (and will) happen. The world of Dominions 3 is not Disneyland.