Question

If a magnet could swing freely, what would happen to its north-seeking pole?

Answer 1

You clearly identified the pole you're talking about as the
"north-seeking" pole.  Assuming your integrity and sincerity,
we would then naturally expect that pole to seek north, and
point to Earth's north magnetic pole. 

I'm confident in this answer also because I have several of
these devices hanging from the ceiling of my office, and I can
attest to the fact that on most clear days, they do in fact point
toward Earth's north magnetic pole.