I'm currently building custom gray and black tanks for a 64.
In the old days (I say that since I don't have the years memorized) the black and gray tanks would be below the floor (though some black tanks were above). The tank would be wrapped in fiberglass, and then another steel pan would hold the tank to the floor. A pipe would come off the furnace and enter the black tank area. This pipe would channel warm air from the furnace to the tanks to keep them from freezing.
Depending on the setup though, you can also get tank heater pads. These are flat pads that can run off of either 12v
or 110. They would be run by a switch or thermostat. There are benefits and drawbacks to both systems, though I think there are more drawbacks to the pads. I installed a heatpump with heat strip in my trailer, and will mount my tanks to the floor and wrap them in mylar bubble sheets, but have not decided to put in the tank heaters as I just don't want to deal with the expense right now, and it doesn't get that cold for us. On really cold nights, I plan on just adding antifreeze to the tank, and keeping it as empty as possible. since it will have no insulation between the floor and the tank, I expect to get some heat transfer through the floor, and since the tank wall is 1/4" thick, and I'm wrapping all sides except what comes into contact with the floor, I expect to be able to handle all but the worst of the Virginia weather. That being said, I would feel better if I spent the $600 or so on tank heaters. I've just made a decision not to.
If your fresh water tank is in the trailer, you shouldn't have to worry about that one.
You will want to think about your fresh water hose inlet though. That should be wrapped in some sort of heat tape.
Lastly, if you're on full hookups, and leave the gray open, I would wonder if the actual "stinky slinky" would get gray water ice build up as it is outside and unheated in those conditions.
Finally, Airstreams are not designed for long term sub freezing temps. It's just something to think about. They have a minimal wall thickness, and lots of thermal bridging. I've had some inside storm windows made for my jalousie window, but other than that, the walls and windows get really cold.