I think you might be conflating a bunch of different topics here so I'll try to parse it out for you.
If you mean "Snowball Earth" you are way off in terms of the age. That's hypothesized to have been around 580 million years ago and it was probably induced by a number of factors that may have had little to do with greenhouse gases like CO2. But CO2 may very well have helped the warming (You can learn more
HERE)
Now, as for the 3-5 million years ago, that's still pretty firmly in the Cenozoic Ice Ages we are currently still in. Those were driven in no small way due to
Milankovich Cycles which relate to the orbital obliquity of the earth and account for why we have glacial-interglacial-glacial-interglacial cycles at this time.
Right now we should be heading back into another glaciation event (again, NOT a "Snowball Earth" scenario) but strangely enough the temperature is going in the WRONG WAY.
If we look around at the various drives we know of for the climate nothing that is a "natural cycle" seems to line up sufficiently to account for the CURRENT WARMING.
But human activities DO. They do it quite well!