Is a work trailer cover by homeowners insurance?

A trailer is not covered under a homeowners policy whether or not it is used for work. You need to purchase a seperate policy to cover this type of property for physical damage coverage. While it is being towed and attached to a vehicle the laibility coverage from the vehicle extends to the trailer so if you back it into someone's car the towing vehicle's liability insurance will pay for the damage done to the other person's car.