You shouldn't base it off how old they are. You should first take a test run. Show them a horror movie. If they are fine with it then you know it's okay. If they aren't, then you know they are not ready yet. It's about maturity, not so much age. Hoped this helped.
Theres not really a specific age you should begin watching them. It's the person's authorities' choice. Though, as you've been told it should truly be based on maturity. I've been watching Horror films since I was born. Personally, I think it's better that way; it makes you mentally stronger. At least it has me. I'm 16 now and horror films are my favorite. The only thing that has ben restricted from me is Rated R for sexual content/nudity. Rated R for violence and language has never been an issue with me. I believe it truly depends on the film and the authorities' opinion on the person's maturity. ( :