Depends on your policy. If you have fully comprehensive car insurance, then you would most likely be covered from just about any damage, including storm damage. This type of insurance would cover you from just about anything that can go wrong including theft, graffiti, weather, animals, acts of God. Just about anything, except war.
Lesser insurance that only covers liability or the legal minimum in your state will probably not be as comprehensive.
Also, remember, you only get what your car is worth, not what you paid for it. They will not buy you a brand new car as a replacement, but will give you the current, depreciated value of the car. If you are concerned, get a car insurance quote or consult your agent.