The Nadir and Occultation for MArs Discovery (NOMAD) instrument suite aboard ExoMars/Trace Gas Orbiter spacecraft is mainly conceived for the study of minor atmospheric species, but it also offers the opportunity to investigate surface composition and aerosols properties. We investigate the information content of the Limb, Nadir, and Occultation (LNO) infrared channel of NOMAD and demonstrate how spectral orders 169, 189, and 190 can be exploited to detect surface CO2 ice. We study the strong CO2 ice absorption band at 2.7 μm and the shallower band at 2.35 μm taking advantage of observations across Martian Years 34 and 35 (March 2018 to February 2020), straddling a global dust storm. We obtain latitudinal-seasonal maps for CO2 ice in both polar regions, in overall agreement with predictions by a general climate model and with the Mars Express/OMEGA spectrometer Martian Years 27 and 28 observations. We find that the narrow 2.35 μm absorption band, spectrally well covered by LNO order 189, offers the most promising potential for the retrieval of CO2 ice microphysical properties. Occurrences of CO2 ice spectra are also detected at low latitudes and we discuss about their interpretation as daytime high altitude CO2 ice clouds as opposed to surface frost. We find that the clouds hypothesis is preferable on the basis of surface temperature, local time and grain size considerations, resulting in the first detection of CO2 ice clouds through the study of this spectral range. Through radiative transfer considerations on these detections we find that the 2.35 μm absorption feature of CO2 ice clouds is possibly sensitive to nm-sized ice grains.