Well stated. The snowball earth phase was special in a couple of ways. First, a planet covered in ice and snow all the way to the equator would have an extraordinarily high albedo - which means that most incoming light would get reflected straight back out at the same wavelength it came in. Keep in mind that CO2 only has an effect on thermal infrared, the generation of which requires the light to be absorbed at the surface and converted to heat. So, under those circumstances much more CO2 is needed to get the same warming effect. Second, at the time the earth actually froze over CO2 in the atmosphere was very low. But the freezing both drastically reduced land-based plant life, and isolated atmosphere from ocean. This left CO2 from volcanic sources free to build up in the atmosphere over millenia, until a tipping point was reached where the equator began to thaw. From that point there was a very rapid positive feedback: thawing --> lower albedo --> more heat absorbed --> more IR trapped by high CO2 levels, allowing temperatures to make that massive jump. The newly opened oceans and regrowth of terrestrial plant life eventually brought the CO2 levels back to a more sane level, and things settled down.
Would not have been a particularly fun time to be around.
