It definitely matters. The need for a filter is to correct for the color temperature of the light available. The color temperature of HID lights seems to normally run in the 3800K to 4500K range (I've seen claims of color temperatures up to 6000K or even 7000K). By contrast the color temperature of halogen lights runs in the 3000K to 4000K range.
That suggests that halogen lights are a little bit, and perhaps quite a bit, warmer (more reddish) than HID lights. That in turn implies that HID lights more nearly represent the color of clear-sky noontime daylight.
However, and this is something that I've just been experimenting with, if you are recording images digitally, most advanced amateur through professional digital still cameras and video cameras allow you to set the white balance right there under the conditions under which you are shooting. Just take a white surface (a dive slate works pretty well) with you, turn your lights on, aim the camera at the slate (so it fills the frame), and set the white balance. Voila! Whatever lights you are using will correspond to "daylight".
Hope this helps,
Jim
