Can you provide more input around this? Is the car Bluetooth OEM or third party? Have you looked at the settings of your car BT to see if that is a native setting to enable? For example with Ford SYNC you receive an on screen message that a new test was received but still have to give it a voice command in order to ready the message content.
In some cases, to have messages read out loud it will require third party software to read them out loud. However, there is also an option under Settings -> Accessibility -> Vision to also ready them out loud. If connected to BT it should push them across. But this is probably not exactly what you are waning to do.