Is the cost of having my car towed covered by my auto insurance policy?

It can be.  If you add towing and labor coverage to your policy then not only can you cover the cost of a tow, you can also be covered for the cost of having a repair shop send a truck to your stranded vehicle to help you get it started or repaired out on the road.  There are several options to this protection and for the most part it is a great value for you.  Read more about it here.