Was the whole Earth once frozen solid?

Possibly, yes. The Snowball Earth hypothesis says that at least once, Earth's surface froze almost completely, with little or no open water. The best candidates are two great glaciations in the Cryogenian Period, roughly 717 to 660 and 650 to 635 million years ago. The main clue is rocks left by glaciers that formed near the equator. It remains a hypothesis: opponents question the evidence, and some scientists favour a "slushball" with a thin belt of open water at the equator.

The mechanism is a runaway feedback. Ice is white and reflects sunlight, so more ice means more cooling, which means more ice. Models suggest that once glaciers reach within 25 to 30 degrees of the equator, the ice races the rest of the way. In the 1960s the Soviet climatologist Mikhail Budyko found exactly this in a simple model, and concluded it must never have happened, because he could see no way to escape.

The escape came in 1992, when Joseph Kirschvink, who coined the name "snowball Earth", pointed to volcanoes. They keep breathing out carbon dioxide even through the ice, while frozen rocks can no longer absorb it. Over 4 to 30 million years, the gas would pile up, possibly to around 350 times today's level, until the greenhouse effect finally won and the ice melted, perhaps in as little as a thousand years.

The thaw may have changed life itself. The snowball episodes came just before the first great bursts of complex, multicellular life, and the last of them may even have helped trigger it.