Sorry I don't know anything about geothermal works.  My approach was to use FLOATING deicers but insulate all around to keep in as much heat as possible.  There are several other insulated trough boxes on the BuildItSolar website.

For geothermal, I would borrow/rent a well-auger (one-foot diameter?) and dig as deep as is convenient. Drop in a loop of plastic pipe and back-fill with smooth mud.

The down-flow leg should be insulated (cold sinks) and the upflow leg should be exposed to the 50F-degree soil (warm rises). Cold sinking leg should draw from the bottom of the tub, and the warm rising leg should spill to a level under the water-line near the top.

Put a Small savonius VAWT inline with the warm water exhaust, with the bottom of its shaft spinning a tiny crude propellor inside the up-tube to help boost circulation. Google image search "VAWT", and you could make one from a 5-gallon bucket.

If you trench the pipe run (instead of a vertical well), make sure it slopes up to the tub, so no air gets trapped at the end. VAWT is optional for a proper vertical well, but for a horizontal trench-run, I'd definitely include a mini-VAWT circulation pump.

Passive solar MIGHT average 6 hours/day useful output.  Between the short days, and so much lake effect snow, I'm gonna have to be running electric heat the other 18 hours/day.

Also, I'm already renting a trencher for another project, if 5 1/2 ft will get me to a reasonable temp, I think I'll avoid having to rent the well digger (which I found to be impossible anyway.....when I wanted to put in a new well).

The insulating thing might be good, but I'd like to be able to eliminate the electric heater completely.  The barn (which also contains my office) is fed by a single 20 amp breaker, and I have to un-plug the silly heater to make coffee....which is not a big deal, except when I forget to plug it back in.

Some solar heated (or not solar heated) insulated tanks that people have tried are described here:
http://www.builditsolar.com/Projects/WaterHeating/water_heating.htm#Animals

Some of these have a season or more of use on them, and generally the results are good.  The tanks heat up enough during the sunny periods to store heat and not freeze for quite a while -- days, depending on the temperatures.  The insulation and small open water surface help this.

This is the one I made for my neighbors horses -- it worked well enough last year that we made no changes to it for this winter -- she thinks its great:
http://www.builditsolar.com/Projects/WaterHeating/SolarHorseTank/SolarHorseTank.htm

It seems to me that the geothermal should work.  You would need to get down far enough to get to dirt that stays far enough above freezing to make a difference.  Around here, the ground at 3 ft down in mid winter is at or near freezing, so it would have to be deeper than that to do much good (for our locations).

If you do the geothermal, please report on how it comes out.

I think that just insulating the tank well and limiting the open water surface area would cut the heater on time dramatically.