Any damage to the trailer is only covered on a specific policy bought for that trailer with Comp / Collision coverage purchased.
Any liability when set up fall under either home owners insurance, vacation liability or full time package on the trailer's policy.
Any liability when towing (connected the car) comes from your car's policy.
If you don't owe money on the trailer you don't have to insure it. The reason you would want to is if you want damage coverage for the trailer itself and or extra liability while vacationing (don't own a home).
