A metal enclosure may shield the contents from an EMP's destruction
It is important that you understand that the insulating effect of the rubber tires is not 100% effective for EMP shielding. A fiberglass body or being parked too close to a large metal expanse (next to a metal wall, for example) will make a vehicle more susceptible to EMP. Also, as almost all new cars are heavily computerized and filled with IC circuits, the newer the car the more likely that it will be out of commission following an EMP weapon burst.
It is for this reason that many who practice survival preparedness have a backup survival vehicle. These vehicles are usually pre-1980 or earlier, also an older diesel-powered vehicle should still be operable as they dont use fuel-injectors.
The technology is developing steadily to provide effective EMP shielding for newer vehicles. Unfortunately the technology is still limited to military applications, and has not really been applied to vehicles available to the public.
Overall it appears that your best bet for ensuring you have an operating vehicle after a high-altitude EMP burst is to have an older diesel car or truck. Make sure its sitting on good rubber tires and not parked next to a metal building.