I was wondering how it is possible that Jack Nicholson wasn't nominated for his acting in The Shining.
Did any actor ever win an Oscar for their work in a horror movie?
Of course they did:
Ruth Gordon won Best Supporting Actress in Rosemary's Baby.
This article lists 14 horror films "noticed" by the Academy, including Misery and Silence of the Lambs. Whether these two can be classified as horrors is arguable, but if so, you can also add Kathy Bates, Jodie Foster and Anthony Hopkins to the list.