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.