During the Pleistocene Ice Ages, the level of CO2 in the atmosphere dropped by about 100 ppm relative to pre-industrial values. This drop intensified and perhaps prolonged them due to the decreased greenhouse effect (about 2 C of the 6 C cooling associated with the ice ages).
Increased solubility of CO2 in the Ocean due to cooling is a large and obvious effect, but it is roughly balanced by two opposite effects: decreased solubility due to increase salinity and the destruction of biologically incorporated carbon by glaciers and increased aridity of the continents.
Three other effects seem to play the crucial role. First, the biological pump that rains carbonate shells on the sea floor appears to have been more effective during ice ages, due multiple effect, possibly including transport of more iron laden dust into the Southern Ocean. Second, the rate of ocean overturning seems to have slowed, allowing CO2 to spend more time in the depths, and finally, the oceans appear to have been more acidic (less basic) during the ice age, decreasing the rate of dissolution of CaCO3 in the deep ocean.
Source: Bender, Michael L. (2013-08-25). Paleoclimate (Princeton Primers in Climate) (Page 193). Princeton University Press. Kindle Edition.
Summary (for Lumo): It's complicated.