Lawl, the poles switch all the time from frequencies of maybe hundreds or less to millions of years at random and have never been found to be linked to mass extinctions. As far as I'm aware it has never even been found to have a causal relationship with climate change on any scale, let alone full on ice ages.
Yes the world will end but everything else you mentioned there is bollocks. People equate the world ending with humanity dying. If we die before the world ends is hard to say or if the world will end but we won't. Either way, in a few billion years the Sun will become a red giant and destroy the planet.
An ice age certainly wouldn't kill us off. It could drastically reduce our numbers and cause serious havoc but we could survive better than practically any creatures of similar size. Humans can live practically anywhere on the planet, from the desert to Siberia.