Hello Tony
You are correct that burning LPG you produce water vapour, but that is actually true of burning any Hydro-Carbon fuel, it is a by product of combustion.
Most caravans soldin the UK were fitted with heaters manufactured by Carver or Truma. A feature of all the heater products from these manufactures is that they are "Room sealed".
This means that air for combustion is drawn through a tube from under the caravan, it is mixed with the gas and burnt inside a heat exchanger, and the products of combustion (including the water) are expelelled throuhgh a flue pipe to the outside.
This arrangement is very safe provided the heater and flue are mintained correctly. You will only get hot air inside the caravan with no added water or other flue products.
Products from other manfactures may have open flues that could discharge flue products inside the caravan if the flue is blocked.
or Electrolux. Ther are som other minor manufcatuers