I highly doubt that you can run horror in D&D.
Horror depends on a feeling of powerlessness and D&D is hardwired to make PCs powerful, both in how the mechanics work and how the PCs progress. And as everything is tied to level you can't have the PCs not progress and thus become stronger in combat. You have to always use enemies way above the level of the PCs, but that causes other problems as so much is tied to level.
This is also a reason why I think D&D is also bad for modern games. In modern or scifi games (Horro, too) skills become more important as there is more things you can interact with, even if its just because we are more familiar with that setting. And Skills in D&D are imo not very well done, both in how PCs gain skills and how they work (tied to your combat level for example).
And because of HP bloat you also always have the case where the PC can walk through heavy suppression fire just fine, only losing a bit of HP which are easy to replace in D&D, and start punching or stabbing the gunner when in reality you would seek cover and running through it is close to suicide. And because we are familiar with modern settings such differences in behaviour is very noticeable.
The level and HP bloat also affect other things. When a PC is level 10, why would he care what some guardsmen says? They can do nothing against him unless they suddenly turn into level 10 guards for no reason. And in a war game you also have the problem that the PCs can only ever meet level appropriate enemies even in a chaotic field battle because enemies of lower level are no threat and (much) higher level enemies guaranteed TPKs.
Heists are imo also not very well done in D&D because of the skill issue mentioned above and because of the PCs staying and combat power, so very often "cracking skulls" is a valid and usable solution, supported by the game mechanics, which goes counter the idea of a heist.