I was going to comment earlier, but didn't want to kill the thrill.
The issue isn't the heat exchanger, but the power practicality. Like your car coolant system, it only works with the engine running and the water pump moving water around.
How exactly do you intend to power the system? You would have several options, all of which would have an immense amount out waste. 1. You have a 20 gallon tank added to your truck, so as you are driving you can be using the heat while driving to your destination heating the water.
I don't think you want to do this one, do you? You want a raw water intake source, like a stream, that seems to suggest a stationary posture. That means you need to be constantly running the vehicle to do this...
You appear to kinda want a ON DEMAND water heater via your car, and I am not sure the efficiency is there. The amount of unnecessarily wasted energy via the engine running would be intense. You are honestly better off looking at a solar shower solution.
Those things work incredibly well and can take freezing cold water, using solar energy, heat it up to a usable warm shower.