Answer: I definitely can be an oxymoron, but there are also some scenarios where it doesn't have to be an oxymoron, if it is used correctly.
Explanation: In a more literal sense of the phrase, it might be able to refer to the type of light from the moon that, while it can be bright, is not quite bright as the sun's light. The moonlight also has a tendency to cast far more shadows in the world than the sun does in daylight, thus giving the impression that this "Dark moonlight" gives offs its own shadows.
In a more figurative sense, perhaps it can refer to the more ominous and mysterious type of lighting and shading that moonlight casts as opposed to the joyous and brilliant glare of the sunlight. "Dark moonlight" can also convey a sense of the unknown, the supernatural or even of horror.
So yeah, while it is oxymoronic, in the right context and application it can be truly profound. Anyway, hope that helps, and have a great day!