I think you very much could run horror in Daggerheart. The Stress system is right out there on the table to start things off. What I would do is start of by causing Stress to the character attempting an action any time they succeed with Fear, and to the entire group whenever they failed.
And then, since I own the boardgame Mansions of Madness, I'd open up the Sanity cards and offer reduction in Stress if the card was greater than the Sanity value, but have the card take effect if it was less than or equal to it. I'd probably have to do some work on the actual mechanics, but if you want a game where characters can go crazy, well there you are.
That's a build-out of the game, and I'm sure people can say, "Well, why not play a horror themed game if that's what you want?" And I'll answer the same way I do whenever anyone wants to add to a game: if you like the core of a game, why not use it and bolt on the extra? If you don't like the mechanics or a horror or investigative or ... fill in the blank game, why not play what you like, and add the elements you don't have to taste? As my friend Egg says in Big Trouble in Little China: take what you want, and leave the rest.
There seems to be a discussion of taking armor or weapons away as being necessary for horror. I haven't seen much of that discussion due to, I assume, being on ignore for some of the participants. I'd say that you definitely can have armor and weapons and still have horror. As Newt most famously said in Aliens, "It won't make any difference."
There are tons of good resources out there for running horror games and I'd recommend looking in that direction. As an old person, Gurps Horror is a fantastic resource. The key elements of horror are a loss of the feeling of control, the unknown, slowly building tension, and mental/body horror. And since I'm just writing this pretty casually, I'm sure that I'm missing out on that. The key is that I'm saying you can put people into scary situations by removing their assumptions.