An exactly Earth-sized tidally-locked planet orbits its host star, which is functionally identical to our Sun, at an average distance of 1 AU, the same distance that the Earth orbits the Sun. The atmosphere of this Earth-sized planet is identical to ours in every way.
Carbon dioxide freezes at -109 degrees Fahrenheit/-78 degrees Celsius/195 degrees Kelvin. Does the side of this planet that faces away from its star reach temperatures low enough to form carbon dioxide ice caps similar to those on Mars?
Note that, since this planet has an atmosphere, atmospheric convection will draw heat from the star-facing side to the opposite side; this might make it too warm there for the formation of dry ice.