The greatest regional sensitivity of climate models to changes in global radiative forcing appears to be in the Arctic, where sea ice and snow cover are highly variable seasonally and interannually. Clouds are thought to play a significant role in the Arctic climate variations through ice-albedo feedback processes. Because of the typically small contrast between clouds and snow or ice in the visible and infrared window channels, it has been difficult to monitor cloud properties accurately in polar regions on a long-term basis. This difficulty can be mitigated to some degree during sunlit conditions by using near-infrared (NIR) channels available on research satellites and the Meteosat SEVIRI. The MODerate-resolution Imaging Spectroradiometer (MODIS) has several relevant NIR channels that can be exploited to retrieve cloud properties over snowy surfaces including sea ice. The Clouds and the Earth's Radiant Energy System (CERES) used the MODIS 1.6 and 2.1-µm channels on Terra and Aqua, respectively, to retrieve cloud optical depth over snow and ice for its Edition 2 and the 1.24-µm channel on both satellites for its Edition 4 processing. Cloud effective particle size was retrieved using the 3.8-µm channels in all cases. Long-term measurements are possible using Advanced Very High Resolution Radiometer (AVHRR) data on the NOAA and MetOp series of operational satellites. The AVHRR complement measures reflected radiation at 0.65 and 0.87-µm with either a 1.6 or 3.8-µm channel. This complement limits the retrieval potential for clouds over snow. To better understand the limitations and develop an optimal retrieval system for a given set of imager channels, this paper performs retrievals over the Arctic and the ARM SGP site with Terra MODIS data to study the sensitivity and accuracies of optical depths retrieved using the 0.65, 0.87, 1.24, 1.6, and 2.1-µm channels. Additionally, infrared channels are used to measure the optical depth of thin clouds over snow. The results are compared to independent measurements taken at the ARM SGP and NSA surface sites. The overall goal is to develop optimal retrieval systems to cover a full range of optical depths over snow or both historical and future satellite observing systems.