Of course, this all presupposes that the pole is shifting, rather than the pole staying in place, and the earth shifting. A shift, or tumbling of the earth would explain colder winters and hotter summers, for example.
Yes, the earth does precess about its axis:
http://www-istp.gsfc.nasa.gov/stargaze/Sprecess.htm
And as you can read on that site some see a link between the precession and ice ages. But, the earths north magnetic pole has moved nearly 1,100 km in the last century:
http://www.physorg.com/news8917.html
I am no expert on climate, but I would suspect if the true axis of rotation of the earth had moved that far there would be huge climatic changes.