Take your time at the beginning. Most horror movies have a slow build. There is also a bit of time before the scary things start happening. Use this time to set up your characters and relationships and only hint at the horror. After all, the more we care about your characters the more we will want them to succeed and the more we will feel the wrench if they get sliced.
Start small and build. In most horror, there is a real build in not only the level of things happening, but the tension. The first scary things that happen (such as books falling off shelves, a dead bird being found, etc) are barely noticed by the protagonists. Practice building tension. Tension is hard to maintain in a comedy show as laughter is a big releaser of tension.
The same is true of the protagonists fear. Obviously they must be afraid otherwise the horror has no impact, but it can start small and build. Your character will be terrified, but you don’t have to be so from the start. It’s tiring for the actor and it’s tiring for the audience.
In movies, there is often a scare at the start: a kind of prelude to the coming horror. But the main reason for this is otherwise, there is 30 plus minutes with very little horror which is hard on a movie audience who wants the horror now! Unless you are doing a 2-hour show, you don’t need to worry about doing this, although it is an option to have a little taster of what’s to come.
Scepticism is allowed. Normally being sceptical or not believing what is happening or being said is a real killer for improv scenes, but it’s okay for the protagonist to be sceptical in the early stages of the horror. It is very much in the genre for the hero to not pay attention to the books falling off the shelf, or to attribute weird sounds to everyday occurrences. In fact, there’s a built-in game of scary thing happens and giving it increasing implausible explanations. Of course, at some point the protagonists must realise the horror is real.
Allow characters to die or disappear. But again, don’t rush this and remember this is a big moment.
You only need one type of monster. Improv stories tend to have too much of everything, and improvised horror is no exception. You don’t need to have a vampire and a werewolf and a zombie and haunted clock; you only need one.
Sometimes it’s scarier not to show it. Makers of low budget horror movies have realised that they can’t compete when it comes to special effects. But they don’t have to compete. Some of the scariest movies have hardly shown, or not shown at all, the monster. It can be more effective to show someone scared of the gorgon or someone recoiling in horror at the sight of the gorgon than have the reality completely destroyed by someone pretending to be a gorgon. (See especially The Blair Witch Project (1999), Paranormal Activity (2007) and Night of the Demon (1957).)
Do not play just for laughs. There has to be some jeopardy and some fear. Depending on your show, you might go more for the jokes, but you need characters to be scared. If it’s all jokey, then it’s a lame parody of horror. Given that most improve is dedicated almost entirely to getting laughs and little else, the more scared you allow your characters to be, the more like a real horror show it will be and the more your show will stand out. My advice would be to rehearse pure horror cos your team probably doesn’t need to practice the funny and when you have an audience the funny will slip out of its own accord.
The evil can be defeated. Finding a way to kill it, remove it or send it back to whence it came is an important part of the story. It gives the remaining characters hope. It doesn’t mean you do kill it, it means you can try. In many stories, you will succeed, in others you fail. However, even if you succeed, you might do so only to find that was just the tip of the iceberg or you merely angered something bigger and scarier.
Have fun. Enjoy playing a scared character. Enjoy being frightening. Enjoy being part of a rich story-telling tradition.