Not intentionally, I didn't.
I was a really good reader and had read most of Steven King and James Herbert books around that age.My parents were lax (1970's) and I had a television in my bedroom, so watched a lot. Stuff from the books would bother me more.
What really scared me was seeing the bombing of Hiroshima on television, that stayed with me and the threat of being bombed for years.
Some Parents don't filter the News.
My Mum did a lot of childcare for me and my youngest, in particular grew up watching CSI and the like. Then my Mum thought Donnie Darko would be OK for her at around 8, because it had a rabbit in it. She watched Poltergeist with me at around 10. But not much else, except Dr Who type stuff. I wouldn't have deliberately chose a horror film to watch with her. At that time we were watching newly discovered Anime.
She wasn't bothered about what she saw and shares a love for horror films, with me and my Mum.
I think that I should have been shielded from the casual sexism more than the horror stuff, tbh. Although we watch Horror Films together, I avoid anything with sexual stuff in.