Asking for horror anime with those restrictions is self-defeating too. What has too much action is subjective. i just recommeded good horror anime. 

Idk Deadman Wonderland and Hellsing seems pretty tame to me. I watched and enjoyed them, but I would not recommend them as horror.

This is coming from a guy who does not watch horror movies at all.

I somewhat agree since hardly any anime that's classified as horror will give a rational adult good scares often ... 

I hope Roronaa will see my recommendations ...

Ajin 

Seraph of the End

Blood+

I would also like to try out the Terraformars manga instead of watching the anime since I heard that it's much better and I have yet to check out Ga-rei: Zero ...

That's odd. I would have figured that Highschool of the dead would be the one some might consider not to be a horror anime. Yes, it has zombies but it doesn't have any sort of scary vibe to it. It's closer to a late night B thriller with lots of T & A in it. It's still good though. 

There's no real horror genre that's been established in anime or not much of one to speak of. On some anime sites, there's no horror option to select within the genres. 

I didn't watch Highschool of the dead so no comment given for it. For all I know it could be the scariest anime out there :P.

TBH when I was younger I even got scared of Inuyasha and Case Closed (Detective Conan) lol. But clearly not horror to me anymore.

You should! It's fantastic!

I actually finally got around to watching Madoka recently...after being on the fence for a while. I'm a wuss when it comes to stuff like that, but I really liked it overall. My only advice it to watch it in as few sittings as possible, since the story has more impact that way. 

Don't forget to watch the movies afterwards. The first two are well made recaps of the series and the 3rd is the continuation and end of the story.