I think it depends on the game. When it comes to a horror game like the newer RE games, you want to hear your surroundings. If anything I find it more scary to be in a dark room with no music, because you don't know what to expect. Sometimes music can be overbearing as well, and defeat the purpose of a good scare, and some games utilize the same sound or music too much, like the violin sound that everything uses now, which kinda hurts the scares going forward. With horror movies for example, I almost prefer silence, because when you hear that creak of a door, or eerie sound in the next room, it seems to instill a lot more fear, but also adds to the dread I think.
With Silent Hill, it worked because the music wasn't constant and worked differently depending on the area you're in. I remember Silent Hill 2 having sections with no music, and just sounds of monsters and metal sounds. Sometimes silence is enough.
I watched this video recently on The Shining. I know it has nothing to do with video games, but I think devs could learn a thing or two about music and horror. Because the way they did the music for The Shining, was pretty cool. You can watch that video below.