Safety in numbers only applies if you can trust the others
Are you familiar with the game Werewolves of Millers Hollow? If not; it's basically a game you play with 10-20 people. Each person is either a citizen or a werewolf. The game is divided in "night" where people close their eyes and the werewolves secretly pick a victim who leaves the game and a day-phase where everyone (including the bad guys) bicker and argue and then together pick another person to leave the game. Despite being played with 20 people, you don't get that feeling of "safety in numbers" at any time, because you don't know who is on your side. It becomes a game of "you versus the world, and some of them can turn into monsters and eat you".
If you play the game with the cards open, it would not be scary, nor exciting, nor a challenge. But because you play with the cards closed and can't trust people, it suddenly becomes challening and the entire feeling of being "a group of citizens fighting the werewolves" is gone completely. Even though you are a group in the end.
Play with hidden objectives and alliances
So I guess the way to make play dreadful is if you hide everyone's objectives and alliances. At the start of the game, give every player a secret briefing which contains hidden information on their faction, their objectives, etc. Make sure that it's clear to everyone that not everything is as it seems. Make sure that briefings are full of lies, too. Remember that not everything you know is true; just because you think that character X is secretly an evil cultist doesn't mean he is. But the fact that you think he is, will change how you play, which will change how character X plays (because he's not trusted, but he knows he's a good guy, so you must be secretly plotting against him, right?
Make sure some of the factions are not immediately obvious. (This can be a player who is an evil cultist, but it can also be a citizen who is an undercover Majestic operative, it can even be a citizen who just really hates a specific person in another team and wants them dead)
Optionally you can give these briefings out randomly to take away any idea of GM favoritism.
Include a side-room where people can get away from the others to discuss things in private. This will immediatly make others distrustful of whatever goes on in there, even it's just tea and biscuits. Occasionally, as a GM, ask players to join you. You can either give them secret info or just ask them if they're having fun. Whatever you do, when they come back out, everyone will be suspicious. Nobody will believe that the GM just took you aside to ask you if you were enjoying the game.
Make sure that information becomes available from time to time that shows the players they really can't trust anyone and they are absolutely right to keep their motivations hidden.
Force players to pick people to trust, even if they can't
Once everyone is suitable suspicious, make sure the game has opportunities where you cannot help but trust others to help you. At some point, you'll probably have to go in guns-ablazing and shoot some cosmic horror. But if you have to divide 5 rifles under 10 people and you know at least 2 of them will shoot you in the back at the most inopportune moment, you'll get a lot more anxious about the whole experience.
Pick a horror that is relatebly human and preferably played by one (or more) of the players
If the horrible being you have to fight is a cosmic green alien who breathes fire but exists only because the DM tells you about him, it's hard to be scared. If the cosmic horror is instead a skinwalking demon who leaps from body to body, devouring the soul from the inside before moving on to his next victim, and he's currently occupying the body of what was once Jim, and you just told Jack and Tina that you trust Jim and they should take him along on their trip, and you realise this just after they've left for the off-side room and you can't follow them, and you don't know if they'll come back out, and if they do, whether they'll still be themselves, that's quite something else.
It also means at some point that you might have to kill one of your friends' characters because you think he's a demon. But you might be wrong. But if you hesitate, he'll be on to you. Or you might have to hide your suspicions, but he was just trying to convince another character to check someting out with him, and you're pretty sure that other character is on your side....
Giving the players hard choices, and letting them experience the consequences of those choices, will go a long way in setting an atmosphere for a game. Shooting an NPC just means the DM won't talk about them anymore. Shooting another PC means someone will be out of the game. And he'll probably have a few words to say, especially if you were wrong, and player get the option of a good death-scenes before they are gone.
Recruit the dead to improve the atmosphere.
Since it's no fun to be out of the game, make sure you have roles for the dead. Creepy ones. For example, if you kill another player, but he turns out to be innocent, turn them into a ghost. Let them follow the person who killed them around and whisper things to them for the rest of the game. Imagine having "You don't trust him? You didn't trust me either. You killed me. Look how well that turned out. Do you really think this murder will go over better?" whispered into your ear by the person you killed while you are contemplating killing someone.
Likewise, you can recruit dead players who were not so innocent into more creepy roles; whether as crazed sources of information, rerisen as undead or demons, or just as sources of a haunting who can sit near a GM and suggest terrible things to happen from time to time.
Watch this review of a Megagame in action
I've played many games of Millers Hollow, which aren't entirely roleplaying but definately work with the aura of mistrust. But what you're doing is a step more extreme. But nothing extreme hasn't been done before... so I'll link you this video.
It's by the people from Shutup and Sit Down, a boardgame review. In it, they play a game created by a group called the Megagame Makers. It has about 50 players and the scenario is that each group of 4 players plays a country on earth, the scenario is the arrival of alien forces (also played by a group of players).
It's mindblowingly awesome, a good video, and shows how a game like you're planning to do might go. While it's not classical horror, I think it will definately help you, if only with the logistical requirements of a game on the scale you are planning.
If you don't want to watch the whole video, the (surprising) outcome is under the spoiler:
In the end, it turns out the aliens are friendly. They had been claiming this for the entire game. This did not, at any point, stop the various countries from mistrusting each other and nearly unleashing world world three, stealing and sabotaging each other's progress, and sending the world's population into complete panic over a looming alien threat.
If you want more info on the guys who make these megagames and some of their rulesets and stuff, check out their site: http://megagame-makers.org.uk/