This paper describes the modification of land snow cover module of INM RAS climate model. The possible liquid water content in the snow layer and refreezing of melt water are taken into account by modified version of the model. This is especially important for transition season modelling, because of this phenomenon is observed mainly during the formation and melting of the snow cover, when surface temperature fluctuates around $0~^\circ$C. Simulation of snow density evolution is also added. The snow model is verified on observation and reanalysis data, including the ESM-SnowMIP-like protocol. As a result of these updates, mean climate snowmelting periods according to INM RAS climate model are refined, particularly in middle and high latitudes. Snow covered area reproduction is also improved. Modified version of snow model on the land can be used coupled with albedo model of a snow-covered surface, which takes into account snow metamorphism, and it can also be applied for sea ice case.