In this work, we develop a software suite for studies of atmosphere–underlying SNOW-spaceborne optical receiver light TRANsmission calculations (SNOWTRAN) with applications for the solution of forward and inverse radiative transfer problems in polar regions. Assuming that the aerosol load is extremely low, the proposed theory does not require the numerical procedures for the solution of the radiative transfer equation and is based on analytical equations for the spectral nadir reflectance and simple approximations for the local optical properties of atmosphere and snow. The developed model is validated using EnMAP and PRISMA spaceborne imaging spectroscopy data close to the Concordia research station in Antarctica. A new, fast technique for the determination of the snow grain size and assessment of the snowpack vertical inhomogeneity is then proposed and further demonstrated on EnMAP imagery over the Aviator Glacier and in the vicinity of the Concordia research station in Antarctica. The results revealed a large increase in precipitable water vapor at the Concordia research station in February 2023 that was linked to a warming event and a four times larger grain size at Aviator Glacier compared with Dome C.