Hello Nicola,
The simple, answer is yes you can use a 230Vac mains portable TV in a caravan, but, it is not as simple as that. A 230Vac appliance needs 230Vac, so 12Vdc will not do it by its self.
Most caravans (certainly modern ones) are built with two wiring circuits. These are a 12Vdc that uses a battery carried in the caravan, and a totally separate 230Vac mains system that is only active when the caravan is connected to an external mains supply. There are two ways it can be done:-
Firstly and the simplest way is use a caravan pitch that offers a mains hook up. With the correct external cable the caravans mains sockets can be used.
The second method is to use a device called an inverter. These convert 12Vdc to 230Vac, but there are limits. You have to use an inverter that is rated to match or exceed the power rating (Watts) of the appliance you want use. However, the 12V battery only has limiter power capacity, so only relatively small appliance can be used, and it will tend use up the a lot of battery capacity.
Generally it better to use either a mains hook up, or you may find that a modern portable tv designed to run on 12Vdc may be better, though even these will use quite a lot of battery power.