I like the topic but right off the bat I see an issue:
even mammals, were on the planet.
Ice Ages have been along shorter than mammals. The mammals rose during the Ice Age(s), but there were mammals when dinosaurs were around before the Ice Age.
I never really looked into the earth magnetic field but even I have heard of the flip before. You really scaring me, I was expecting something like another planet crossing our solar system, at least we could see that coming. But the Polar flip might explain what always causes the abrupt start of an Ice Age every 25.000 years or so.
There has been more than one ice age, they've been happening since even before the dinosaurs.