You want an ND filter, not an FDL filter (auto wb takes care of lighting color).
If you shoot at 1/60th, as you should, you need to open up the lens in bright light to prevent overexposure and diffraction. The ND filter will do that. IMHO ND filters should always be used in video in bright light.
This statement, from a post above: "I don't think a ND filter will have any effect at all on the image output from cmos, unlike film." is incorrect. All an ND filter does is reduce the light coming through the lens, so you can open the aperture; the sensor type or film is irrelevant.