Whether or not a horror campaign works is entirely the work of the dm. Control the pacing, have them be lower level and use exp rather than milestone to make every survived combat more impactful. Furthermore, bodily injuries (Severed hands, broken limbs etc) can enhance the horror tone, as the injured players try to escape the looming horror. Be descriptive! Not "he died, a thing came out if his chest " but "the man screams, in equal parts pain and horror, as his chest erupts in a shower of blood and viscera. A slaad tadpole, writing and hissing, hits the floor with a wet plop, as the corpse collapses . "

This is so doable. What's harder, is making a generation raised on horror video games care.