If carbon dioxide drives climate, how can these fluctuations be explained?

I wonder if Arctic sea ice extent also fluctuated significantly in the billions of years before we started measuring it

It's a fact! London's famous River Thames has frozen over many times since the earliest recorded occurrence in AD 250. It happened 26 times between 1408 and 1814, and from 1608 to 1814 when the river would freeze and the ice was thick enough, huge festivals called "frost fairs" were held on the ice. During the winter of 1683-1684 the Thames was frozen over completely for two months and the ice was reported to be 28 centimetres thick at London. So why doesn't the Thames freeze over anymore? Well, back then, England's climate was much colder and the Thames was broader and shallower, ran more slowly that it does today and had not yet been embanked. These factors led to it freezing over. Today, ponds in England rarely retain a thin layer of ice on a cold winter's day, let alone the type of ice that developed on the River Thames all those years ago.