Condensation --> Ground Fault
That's all. You probably can't prevent all condensation on an outer wall in cold weather, especially in a thin wall.
There are a few ways to mitigate the problem:
Remove the GFCI/receptacle. Tape (electrical tape only) over all connections/exposed metal parts. Install it again. If the problem is due to condensation dripping down from the top and shorting out just enough to cause a ground fault, that may be enough to fix it because the condensation won't touch the hot or neutral lines.
If the problem is water getting into the GFCI mechanism itself, a simpler (not GFCI) receptacle, preferably weather resistant (to have a better chance to stand up to water, though in this case from the wall rather than from the weather outside) may solve the problem. But you can't get rid of the GFCI protection, so you need to move the GFCI protection to either a previous receptacle in the chain (in a different room or in this room but on a different wall) or to the breaker.
As suggested in a comment, move the GFCI/receptacle from an inside-the-wall box (which is normally best but not here because of condensation due to the thin outside wall) to a surface-mounted box. That will make the entire receptacle be inside the conditioned space (even if you are not running HVAC all the time, it will still be better than the outer wall) and have the entire usual wall thickness as insulation.