The heat pump works by pumping the heat out of the ground. And the soil is a pretty good insulator, so you'll eventually just freeze the water in the soil around the pipes.

It looks like this: one day in winter, the temperature of the coolant in the loop outlet falls below 0C. And after that, it starts dropping down by about 1C a day, until the pump becomes a resistive heater. If you sized your loop correctly, it hopefully happens towards the end of the heating season.

If your ground heat system also provides cooling that's no longer a problem. I have that for my house. It's pretty great. You're basically time-shifting temperatures across the year. Cool temperatures get shifter to summer and warm to winter. The hole itself won't freeze, because you're not significantly pulling or pushing energy down it.

Even without running the AC, you generally will likely get enough heat flux from the surface and (hopefully) from the water table to thaw the ice during the summer for horizontal loops.

I don't have a personal experience with vertical loops.