I'm not good at music theory, but I'm sure there is a "genre" of classical music that ressemble horror movies (something like the Mozart's requiem?). Also you should look at the waterphone which is an instrument used to make weird sounds in this kind of movies: https://www.youtube.com/watch?v=foSJstDFDfg. It's made of metal, filled with water, and you use a violin bow to play.
how old are we talking? The Monster Mash? Ministry's (Everyday is) Halloween? Thriller should count I assume.. usually the term Classical is like Mozart and Beethoven, maybe you mean Classic?