Hello William,
You give two clues, frisstly you gat a lot of air in the system and it takes time for the water to arrive,
And secondly the hot flow is restricted and the cold alright.
My suspicion falls to the non-return valve fitted into the plastic water inlet to the heater. It sounds as tough it has jammed partly open. My guess is that if you felt the cold water pipe between your barrel and caravan it might be warm from hot water running back to the barrel.
The cause of the problem is usually water freezing in the lowest part of the heater and water inlet to the heater, as the ice expands it dislodges the 'O' ring seal on a poppett valve which then jams in the fitting.
Solution, sometimes the valve can be removed and disassembled, the O ring seal put back into place and alls well, but if eth O ring has taken a set or stretched, the valve may be permanently damaged and replacement is the only answer.
To prevent it from happening in future, ensure the water system is fully drained down when not in use and frosts are predicted. If the caravan is being used, then the residual heat from the daily activity should keep it frost free.