You are attacking the problem from the wrong end: literally. Most farmers do not keep their stock tanks deiced via solar, but rather geothermal, but do not let the name scare you. All it takes is to buy a culvert (steel or plastic) as big as possible, and longer then your frost depth. For me here in Maine, that is 4 feet, so I need a culvert that is 5 feet deep.
That culvert gets buried VERTICALLY into the soil so that the heat (57 degrees here in Maine below the frost line) rises up and hits the underside of the stocktank. By insulating your stocktank, and making the surface area smaller so that water is not as vulnerable to the cold, no ice forms.
If you do searches for this, you will find a host of designs online. In fact I found one from Alberta, but it was done with Mining Truck Tires buried in layers, but it is the same idea.
I think I'll just lie down here for a second. And ponder this tiny ad:
Dave Burton's Boot Adventures at Wheaton Labs and Basecamp