MAD87, I found an interesting thread here titled "Climate-Battery-GAHT-for-heating-a-greenhouse" you may like to read. There's a couple people with experience and some good insights I think.
I'm currently planning a winter greenhouse too and have been considering a GHAT system, but I've ruled it out. I agree with BruceM2, there are less expensive and better approaches. It looks to me like the earth beneath is not nearly good enough heat sync to offset the heat loss through any glaze, and in extended cloudy weather it won't be reliable. Another concern I have, is mold.
In my case, I've decided I will insulate the perimeter underground, but only down the the frost line, not the earth's core :). I'll also run some PEX tubing under the soils about a foot, so I can experiment with various water heat sources. If the PEX is ever in the way, I can just move it around.
