Storm Filomena brought a blizzard to the capital on Saturday, leaving more than 50 centimetres (20 inches) of snow and other parts of Spain were blanketed with 50-year record levels of snow.
A 12am-6am coronavirus curfew is currently in place in Madrid and people can only meet in groups of six or less.
Infections in the southern European country have been on the rise since Christmas.
Just under 52,000 people have died with Covid in Spain and more than two million people have had the respiratory disease.
In the spring, Spain was one of the worst-hit countries in the world, with hospitals overwhelmed with coronavirus patients.
In a bid to break up the snowball fights - which also saw people throw street furniture such as bins at each other, police vehicles were driven between the crowds.
At least four people have died in the record snowfall, while thousands of others were left trapped in their cars or at train stations or airports when the blizzard hit the centre of the country.In Madrid, a 54-year-old man was found dead under the flurries.
Emergency crews in central Spain have cleared 500 roads and rescued more than 1,500 people stranded in vehicles as the country slowly shovels its way out of its worst snowstorm in recent memory.
Madrid’s Adolfo Suarez Madrid-Barajas International Airport, shut since Friday night, remained closed on Sunday, along with railway lines crossing the capital, and more than 150 roads were still impassable.
Storm Filomena lost strength as it moved eastwards but authorities were still urging people to remain at home to limit the risk of falls on icy streets ahead of a severe drop in temperatures in the coming days.
Spain’s weather service forecasts temperatures to drop as low as -14C (6F) in the eastern province of Albacete by Tuesday.
Army emergency brigades are focusing on clearing access to Madrid’s main fresh food distribution centre and to hospitals as Spain also grapples with the coronavirus crisis.
Interior Minister Fernando Grande-Marlaska said the government will take extra steps to ensure that the country’s weekly shipment of the Pfizer/BioNTech coronavirus vaccine on Monday can be distributed to regional health authorities via police-escorted convoys.