Is a feedback mechanism at work in earth's climate system that causes these cycles? Some like to point to possible variability of the sun [very common among stars] as the cause, others hypothesize some cloud of interstellar dust that the solar system passes through periodically. Some look at cyclical changes of the currents in the Atlantic Ocean as being the root cause. In any case the Left will adopt to an Ice Age immediately and ignore any consequential antinomy of their belief system.
Yes there is a feedback loop. When snow and ice can accumulate, that'll reflect the Sun's energy back into space (albedo); a positive feedback towards lower temperatures. Vice versa, less snow & ice (more green vegetation) retains energy.
There's a known 26,000 year cycle of the precession of Earth's axis. Sediment cores indicate a 41,000 year cycle of unknown cause. One hypothesis (that I subscribe to) is the 100,000 year cycle is a beat harmonic of those two cycles.
CO2 is positively correlated with temperature. The argument is whether it's a leading (cause) or lagging (effect) indicator.