If that's an automotive light you refer to, it will need 12vdc to drive it, and probably a high Amp-hr rating at that. This translates to higher cost and weight. A NiMH or Li battery might cost $80-120 depending on A-hr rating. Alternately you could get a small SLA (lead acid, like car) for $20 but it would weigh 3-7 lbs. Also. you'd need a charger, and each of these battery types require it's own special charger.
Halogen MR-16 lamps used to be popular for DIY bike lights. Most folks moved on to LED a year or more ago due to better light for the same battery requirement (i.e. cost and weight).
There are many bike lights available which you could buy (which typically include light, mount, battery and charger), that would probably work as well as the fog light you're describing. I recommend a fairly new one that uses Cree or Seoul Semiconductor (SSC) led. These are high-output, high efficiency leds, and they require 3-4vdc to operate, so the battery is less costly and lighter.
Go over to Electronics,L&G forum and read. Also for more sophisticated discussion of this topic try