Generally speaking, your towing vehicle liability insurance will cover your trailer while you are towing. The catch is, you will only have liability insurance up to the amount specified in your insurance agreement. In other words, you are likely covered for damage you do to someone else up to your policy limits, after your deductible, but NOT for damage done to yourself! Damage to your trailer, loss from theft, loss or damage from some other event such as a storm would NOT be covered. Loss from theft MAY be covered on your homeowners policy but you will need to verify this with your homeowners insurance to be sure.
Consider adding collision and comprehensive insurance to cover your trailer. It is usually a fairly inexpensive addition to your auto policy. This way you will be protected against loss.
If your trailer is financed your lender will require you keep collision and comprehensive insurance on your trailer for the duration of the loan.
If you have an older less expensive trailer you may not be worried about loosing the value of it, but for most trailers today, the cost of comprehensive and collision insurance is worth the peace of mind. Check with your insurance companies to verify and to be certain of what coverage you may or may not have.