How much of "the horror game" do you have already planned out? Do you know what your horror is, and how it kills?

One way to handle it would be a sort of existential "you don't know you're dead" horror: Either they keep moving after dying wtihout realizing it, or their ghosts are solid enough to be deceptive to themselves and others. Play it straight for the most part, but don't tell players concrete facts about how dead they are or are not. Have a mechanic for K.O.ing without killing, and have that fade to black on characters who are K.O.'d. They wake up later, ready for the next scene. And...even if they die...they wake up later, ready for the next scene. If you go with it being their ghost, you can have part of the horror later on being discovering their own bodies and realizing they're already dead.

By doing this, even after they die, they fear death, and can be K.O.'d (even unto death).

Depending on how much you want to instill a creeping dread, you can have a degeneration mechanic that makes the dead characters feel worse and worse as time goes on. Or you could have it affect the living characters, instead. Maybe its a permanent (for the duration of the game, anyway; this is obviously a one-shot concept) wounds thing, so they get more and more hurt from injury. When they die, the permanent wounds stop but something else starts afflicting them. Try to keep the difference subtle, and ideally they won't realize there's a correlation between ceasing to suffer permanent wounds from getting injured and the onset of random afflictions.

Wait for them to get cocky about how the DM isn't "letting them die" and the like to show them the first body of one of those who did die.