Horror has always been a tough sell in D&D. To truly bring a sense of horror, especially classic gothic horror, you need to instill a sense of helplessness in the face of the supernatural. D&D is designed as heroic fantasy, where the player characters are expected to kick evil in the face several times before breakfast. Obviously, this can be a problem.
4th Edition D&D is also designed as heroic fantasy, so it does require a resetting of expectations before starting a horror game. Toning down certain aspects of 4th Edition play, such as the ability to spend unlimited healing surges between encounters, may be required. However, there are many aspects of 4th Edition D&D that make it well-suited for the conventions of the horror "out of the box".
The lack of high-powered divinations in 4th Edition D&D is key. Knowledge is power, and the high-powered divinations of previous editions could easily derail a good horror story. An evil duke who could be found out by a simple Detect Evil. The mystery of livestock being found mutilated in the night being solved by a scrying. Don't get me started with what spells like Commune or Find the Path could do!
Granted, many of these spells exist in some form as Rituals in 4th Edition D&D. Nevertheless, their potency is greatly diminished. Many of these rituals now require skill checks, making them less reliable and adding an element of doubt. All of this is useful when planning a successful horror game.
Another aspect of 4th Edition is that curing disease is a much less certain thing than in previous editions of the game. Disease can be a potent tool in horror. It represents a violation of self that can be played to great effect. This is especially true in the case of a "disease" like Chaos Phage, which is used to represent a young Slaad gestating inside of the character.
In earlier editions of the game, Remove Disease was simply too effective. It also had a bit too much certainty. If you were capable of removing the disease, you always removed the disease without further consequence. In 4th Edition, the cure can be as bad as the disease. A poor roll against a potent contagion can kill the character you intend to save. At the very least, it encourages characters to ensure they are well rested and at full HP when the cure is attempted.
Admittedly, limiting divinations or the ability to cure disease are not all you need for a good horror game. It is up to the DM to set the proper mood. Nevertheless, there is a reason why the old Ravenloft campaign setting limited these abilities. Having them simply made it too easy to regain the sense of control that is anathema to a good horror game.
So I highly recommend injecting an element of horror into your 4th Edition D&D games this month. You might be pleasantly surprised at how well it goes!