In a race-prepped car (i.e., no carpeting, no insulation) long pants are required because there is a chance of burning your ankles, calves, etc. on the hot metallic surfaces of the uncovered areas. In a street car (whether track prepared or not), where there is still carpeting and such, we highly recommend long pants, but do not require it, especially in the summer time. We recommend long sleeves, but we do not require it. So in a nutshell, it's your skin, and your decision.
In all honesty, I have never seen a car fire, even while racing. It's not real likely in today's cars, especially not street cars.
BW