Why would moving the South Magnetic Pole change anything? It's not as if the Rotational Poles moved.
I can't see where it would change much, except magnetic declination on compasses and maps.
There are ice caps at extreme latitudes due to the relatively little solar energy imparted to those regions. The rotational axis of the planet hasn't shifted with the magnetic polar movement, otherwise, you'd have to find something else to blame "climate change" on, besides human activity, unless you could make a case that humans somehow caused the movement of a magnetic field.
Many of the fossils found in icy regions that came from tropical latitudes are from times when the whole planet was warmer, and those continents/landmasses were arranged differently on the Earth's surface (Pangea, Gondwanaland, anyone?).
SO, nope, I'm not buying that stuff.
The one change i can see, is that those organisms which migrate using magnetic fields to do so will likely go off course.