There are of course some store-bought remedies for cleaning magnesium chloride from vehicles. Some will depend on what part of the car you are intending on cleaning, but others it doesn't matter. There are some chemical ingredients in these to remove the magnesium chloride and to prevent any damage to the vehicle.
One such line of products includes Mag Wash. This product and others from the same manufacturer will remove the substance without damaging paint, chrome, aluminum or any other section of the vehicle. It is easy to use, but you should read the instructions before using and wear rubber gloves while washing the vehicle.