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This question is specific to the hot water tank in an RV. In my case it is 6 gallons, propane heated and insulated with the only exterior contact the access panel, as seen in most standard RV's in the US.

Hard as it is to believe hot water can actually freeze faster than cold water. How it happens is not fully understood, but undeniable it does happen. See related posts on physics.stackexchange What is the status of Mpemba effect investigations? & Hot water freezing faster than cold water

Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real.

Source

The RV is currently winterized and located outside in temperatures that are freezing and below. I am leaving from a frozen area, traveling hundreds of miles through freezing areas, and arriving in a warm area (Florida USA). I must flush the fresh water system and top off before departure. Which means my hot water tank will be full. I can either leave it unheated with cold tap water (from my home, temp unknown but not ice) OR I can start the water heater and bring it up to temp before leaving.

All the plumbing and the fresh water holding tank are inside the RV. We will be stopping occasionally and heating the inside of the RV, so no concerns about the pipes or fresh water tank.

Driving with propane heating on (air or water) is possibly illegal and definitely unsafe.

Should I travel through freezing areas with hot or cold water in my RV hot water tank?

Ideally the hot water tank should be plumbed in a manner in which it can be drained without affecting the rest of the system. Typically this means either nothing comes out of the hot water taps when it is bypassed or cold water does. Your best bet would be to flush the system at home, then drain the hot water tank, and then drive with an empty hot water tank. If you need hot water while traveling, you can either fill the tank, heat it, use what you need and then drain the system. While this wastes water and propane it will prevent freezing. The other option is to periodically stop and reheat the water. A hot water tank is pretty well insulated and the water will not require frequent reheating.

it doesn't matter, your pipes will freeze long before the tanks will. At best the Mpemba effect buys you another hour before freezing sets in, however your pipes will simply not take an hour to freeze in freezing temps, so the effect will be very minimal. The solution for long duration freezing temps is to install a re-circulator pump, if your RV is too old to have a battery heated water tank. Another option is to wrap the pipe in heat tape and insulation.

A lot depends on how the water system in your RV works. Some RV's really aren't made for winter use. Others are designed from square one to be usable at cold temps. These will have heat tapes on the plumbing, well insulated water and sewage storage tanks, and drain systems that are easy to access.

As others have mentioned, the pipes are the first things to freeze. But if you have taps where opening the tap starts a pump, then they may be set up that water drains back into the tank when you shut the tap.

You also need to worry about traps in your water disposal system and the sewage tank freezing.

Bottom line: The hot water tank is the least of your worries.

This seems like a contradiction, if you are worried about freezing, then it would be better not to have any water in the tank/pipes where it could freeze and cause problems, and if not then it really doesn't matter whether or not it was hot or cold to start with.

Also, as long as the journey is, it probably won't matter as the hot water will cool down to the same temperature as the cold tap water anyways.