Insulating outdoor caged water holding tank

Get a waterbed heater and put it on the bottom against the plastic tank. They are made to not melt vinyl so it will be safe for the plastic tank. I would suggest that you use a layer of reflectix against the tank and then use a couple layers of 2" rigid house foam (the colder it gets, the more insulation you will need). They make a special glue just for "foamboard" that you can find at Home Depot, amongst other places. This is what we did with a cistern for the spring that was next to our pump house. We used 4" of foam in the Southern Appalachians which was probably overkill for our area.

Using "with an electrical heating element" is the safest way even with lots of insulation.

don,t forget the bottom.make it air tight.

Foam insulating sheets, as thick as you can find, probably 4 or 6 inch with an electrical heating element inside if it gets really cold. Use multiple 2 inch sheets if you cannot find thick stuff. Do not use fiberglass insulation, it's worthless if it gets wet. Have a removable insulated lid to provide access to the tank.

I'd probably wrap the whole thing protective material like 3/8 painted outdoor plywood