When cold, does the body use stored brown fat as an insulator, or does it actually burn the fat for warmth?

Almost neither: Official "brown fat" is only present in newborn babies as a source of immediate energy. As we age, this turns to regular yellow fat as you know it. In order to produce heat, there are more immediate sources of energy that the body draws on than fat. Even over the long haul, i don't believe that stored fat would be used much for energy needs unless circumstances were extreme and nutrition scarce.