Lowe's sells 4x8 sheets of insulating foam board. It comes in various thicknesses (different R Values.)A guy on Youtube used some exterior plywood to cover the top, and attached styrofoam to the underside of the plywood. Naturally he left a cut-out for the animals to be able to drink.
If I went that way, I would start with a 4x8 sheet of the plastic paneling that's used in showers/surrounds rather than tile. It's much lighter than plywood and might stand up to the weather better.
The issue with either solution becomes making certain that there's nothing toxic involved.