As the near-surface atmosphere over the Antarctic Plateau is cold and pristine, its physico-chemical conditions resemble to a certain extent those of the high troposphere where cirrus clouds form. In this paper, we carry out an observational analysis of two shallow fog clouds forming in situ at cirrus temperatures - that is, temperatures lower than 235 K - at Dome C, inner Antarctic Plateau. The combination of lidar profiles with temperature and humidity measurements from advanced thermo-hygrometers along a 45 m mast makes it possible to characterise the formation and development of the fog. High supersaturations with respect to ice are observed before the initiation of fog, and the values attained suggest that the nucleation process at play is the homogeneous freezing of solution aerosol droplets. This is the first time that in situ observations show that this nucleation pathway can be at the origin of an ice fog. Once nucleation occurs, the relative humidity gradually decreases down to subsaturated values with respect to ice in a few hours, owing to vapour deposition onto ice crystals and turbulent mixing. The development of fog is tightly coupled with the dynamics of the boundary layer which, in the first study case, experiences a weak diurnal cycle, while in the second case, it transits from a very stable to a weakly stable dynamical regime. Overall, this paper highlights the potential of the site of Dome C for carrying out observational studies of very cold cloud microphysical processes in natural conditions and using in situ ground-based instruments.