The solubility of water in liquid carbon dioxide has been investigated by Hosmer W. Stone in 1943 from -29 to about 22 °C.
Is there any research done on the solubility of water in liquid $\ce{CO2}$ at still lower temperatures ?
The lower the temperature and higher the pressure, the more soluble CO2 is in water. Pepsi and Coke have staudiesd this for years.