A blanket of snow, when the ground is frozen, is like a layer of protective mulch. Its insulative properties protect both the soil and the plants from desiccating winds and freezing temperatures. It also helps to insulate the plants as they “heave” which can expose their roots to air, as the soil freezes and thaws throughout the winter.
There is something else that happens when it snows: nitrogen is deposited by the snow and absorbed either into the soil food web residing and active at low temperatures or by plants as a result of nitrogen fixation, a microbial activity which, astonishingly enough, can take place even at low temperatures.”
https://www.adn.com/our-alaska/article/blanket-snow-poor-mans-fertilizer/2008/10/09/
If the earth is saturated, the rain runs off; if the ground is frozen, the snowmelt will also run off and most of the nutrients will not be absorbed. In the spring when the earth has thawed and we have a snow, this blanket of snow protects newly emerging plants and leaches nutrients like nitrogen slowly, as it melts into the earth.