Need to buy new head-light bulbs.

Those "HID" halogens are normal blubs with blue tint on them to make them look whiter. The HID kit however replace the old H1/H7 style bulb with a xenon bulbs. This increase the light output but since the housing was designed for a halogen bulb the light is not aimed correctly and will usually blind oncoming traffic. That is one reason why these kits are not street legal. They would be brighter in the fog than halogens but may not make it any easier to see through it because of the unfocused beams. I would just buy some quality halogens like nighthawks or something similar and install some fog lights.