Russia says hurricane winds and heavy flooding have left about 1.9 million people without power in the south, referring also to Ukrainian regions illegally annexed by Moscow.
At least four storm-related deaths have been reported by local media.
Ukraine says 2,019 of its villages and towns have no power after snowstorms.
The storm is also battering Moldova, Georgia and Bulgaria.
Near the town of Anapa, also on the Russian Black Sea coast, a cargo vessel with 21 crew has run aground.
In the capital Moscow, authorities had to deploy specialist machinery to clear the streets after heavy snowfall.
In Ukraine’s southern Crimea peninsula – illegally annexed by Russia in 2014 – Moscow-installed officials reported flooding in coastal areas. Fallen trees and other debris were seen on the streets of several towns.
About 800 exotic fish died when a historic museum-aquarium was destroyed by sea flooding in the port of Sevastopol, the museum director was quoted as saying by a local media outlet.
A state of emergency is now in place in several municipalities in Crimea.
Anton Herashchenko, an adviser to Ukraine’s interior ministry, said the storm “washed away trenches in occupied Crimea that the Russian army dug out on the beaches”.
Russia’s military has not commented on the claim.
Meanwhile, Ukraine’s DSNS emergency service said snowstorms and fierce winds were battering 16 regions of the country.
It said 48 people, including children, had been evacuated from trapped vehicles in the worst-affected Odesa region in the south-west.
As many as 840 vehicles had to be towed away as snow drifts reached more than two metres (6.6ft) in some places, the emergency service said. At least 1,370 cargo lorries are currently stuck.
At least six people have suffered hypothermia. http://gayunggoyang.com/ Traffic is currently blocked on 14 motorways.
Ukraine’s southern Mykolaiv region is also badly hit.
More than 1,500 rescuers are now deployed across Ukraine in a massive clean-up operation. They are being helped by police, border guards and National Guard members.
In the capital Kyiv, the country’s largest flag – measuring 16x24m – had to be taken down from a 90m pole after it was damaged by fierce winds. City officials said the flag would be replaced and raised again.
The extreme weather comes as reports say Russia is again preparing massive rocket and drone strikes on Ukraine’s power grid and other critical infrastructure.
Last autumn and winter, Moscow carried out waves of such deadly attacks, leaving millions of people across Ukraine without electricity and heating.
Last Saturday, Russia launched its biggest drone strike on Kyiv since its full-scale invasion in February 2022, Ukrainian officials said. They said that 74 out of 75 of Shahed kamikaze drones were shot down around the capital.