Moscow Mayor Sergei Sobyanin said on Twitter that one person was killed and two injured after the storm caused a tree to fall, damaging powerlines.
Mr Sobyanin said more than 2,000 trees had fallen so far in Moscow due to the snow and rain.
According to local meteorological authorities, accumulated snowfall reached 62 centimetres deep over the weekend — nearly equal to the total amount of snowfall for the entire month of February in previous years.
In a city where school is rarely ever cancelled, Mr Sobyanin said parents were not expected to take children to school on Monday (local time).
Days of snow triggered a sharp increase in traffic accidents and severely impacted urban transportation.
According to official data, 19 accidents occurred in Moscow on Saturday, injuring more than 20 people.
Moscow roads were congested on Monday morning but the city did not see a complete gridlock as many had feared.
Snowploughs have been working in the city all weekend, clearing a record 1.2 million cubic metres of snow from the streets, Deputy Mayor Pyotr Biryukov told Russian news agencies.
He hailed utility workers for allowing Moscow to function as normal.
More than 60,000 households in regions surrounding Moscow were left without electricity over the weekend but the power supply was restored by Monday.
More than 100 flights have been delayed and nearly 30 flights were cancelled in major airports in Moscow due to the inclement weather.
Russian meteorological authorities forecast the snowstorm will continue to affect Moscow over the next few days, with wind speeds reaching 20 metres per second and temperatures dipping below 10 degrees Celsius.