When I was four, I went to the cinema with my father to watch Alien 3. I loved it so much that my father had to rent me both Alien and Aliens the following days.
I don't know if it's because the child memories or what, but I still watch Alien 3 a lot and I still believe it's frakking awesome as an horror sci-fi movie.
The point is: I don't think children should be forbidden to see horror movies. What scares a child is not the monster, it's the parents' reaction. It's that "no way kid, close your eyes or you will have nightmares" attitude that creates the fear when the kid grows older. I had a cousin that had nightmares when he was like 12 because he saw Men in Black... he had an over-protective mother who always made sure the kid would never see anything with monsters on tv. Instead, I went to see Alien 3 and Nightmare on elm Street part 6 on the cinema when I was less than 5, and I still love horror cinema (although it has never scared me and I'm afraid it never will)
I even remember watching Robocop and Predator on tv instead of cartoons when I was like 1 or 2 year-old. Those movies really give you some strong memories when you're that young, lol