GFCI breaker trips only when weather is very cold
I looked at this again now that it has tripped once more with 38 degrees F outside temperature. It is an AFCI breaker, not a GFCI (or possibly more correct it is both), and when flipping it back to on, the light labeled ARC FAULT comes on (not the other one labeled GROUND FAULT). 

Upon more reading, simply ensuring the microwave isn't underloaded (e.g. add a cup of water to it while heating something small) should prevent this. 

Except that what is funny about this is that when it tripped today it in fact already had a bit of extra water inside. Although it was a shot glass of water, not a whole cup. Now that I'm barking up the right tree I should be able to get somewhere with this though.