Most of you seem to agree that horror campaigns are mostly about overwhelming odds and opposition, meaning big and dangerous monsters for the pc's level. I'm not sure i entirely agree. In my experience, the actual monsters isn't really as important, as the gradual search and discovery process.
In my experience (having played a couple of campaigns and several oneshots of Call of Cthulhu and a few other horror games), meeting and confronting the opposition isn't as "scary" as not knowing what is actually after you. In horror campaigns, ignorance is never bliss... The pc's should be aware or learn that they are followed/watched/hunted or that their foes are so imensely powerful that they don't care about them. Going up against these odds, knowing or slowly realising that the outcome will likely be fatal (or a pyrrhic victory), but also knowing they have no choice as to wether or not to confront the enemy, is usually a good way to create a lovely atmosphere of despair, paranoia and fear. letting the players realize that strange things are happening, not really knowing what or entirely sure why, is another often effective horror gimmick.
IMX Horror campaigns seem to rely on creating a "mood" for the campaign, focussing on feelings of paranoia and fear (defining the genre?). Character interaction also focusses more on this, and campaigns tend to be more rp and investigation intensive, than standard fantasy. I'd asume DnD's timeconsuming boardgame'esque combats makes it difficult to maintain this, so DnD horror campaigns would presumably have fewer combats?
Ofcourse, as a climactic final battle, a strong foe IS needed.
Also, killing pc's left and right doesn't really help to create an atmosphere of fear, as they'll be probably more focussed on being anoyed and thinking about the crunchy details of their newest character build, than care about the game IMO. It also requires tweaking of logic and metagaming for the rest of the paranoid pc's to embrace new characters with open arms every few minutes.