As far as I am aware, the car is treated like any other load you may be carrying. It is not covered itself by most policies, unless it's a car transport policy. Hence uninsured cars can be trailered around without any worries.
Once your insurance policy covers 'use while drawing a trailer' as it's worded here, then you are all good. Should you crash, then the trailer will not be a reason to default on a claim, although it would have to be named on the policy or have its own policy to cover damage to the trailer itself. The 'contents', in this case the car, are usually not covered unless you pay a mighty bit extra.
Ive had everything from a golf, to a VW van on the big Williams trailer, and not cast a thought.