It's interesting that I seem to hear more problems with ASHP than GSHP but that may be because they tend to be much cheaper to install.
My first experience of GSHP was 30 years ago on a big house, offices and garden of a property developer. The pipes were under about an acre of lawn. In deep winter they tried to heat everything, including a pool and stables and this resulted in the soil around the pipes freezing and raising ridges in the lawn. This was entirely a problem of the development company owner not understanding the science and he scrapped the installation rather than accept its limitations and add an alternative for cold weather.
I came across a similar thing when my brother converted an old house into 8 flats, he did not take advice and fitted radiators instead of underfloor, he also used the ASHP for domestic hot water whereas a point of use hot water would have been more sensible. Worse still was because 8 flats domestic hot water was stored in a common tank the temperature had to be raised electrically each day to eliminate Legionella bacteria. Had the ASHP only supplied underfloor heating it would have been adequate most of the time. Instead it was ripped out at great expense.
The interesting thing about ASHP is that the air temperature varies much greater than the soil even only six feet down, so in cold weather the GSHP has less work to do as long as the heat exchange surface under ground is adequate. Both depend on the sun. Oddly a lot of folk seem to believe that GSHP get their heat from the earth's core[1], there is some but it's only about 50mW/m2, the vast bulk is stored up in the surface layers in warmer weather. It strikes me a big pond would be an ideal source as the bottom layer would remain at 4C even as ice thickens over the top.
[1] this reserve of heat in hot rocks is accessed because the hot rocks have been heated for millennia but as the heat is taken out, in Iceland as high pressure steam or low temperature water from flooded mines, the rocks cool faster than the heat coming in from the core, so the heat is not sustainably mined any more than an aquifer in a desert region is mined for water.