Soviet airborne forces jumping without parachutes is a myth that appears to have started in the 1950s. There are three major variations - and lot's of minor variations - to the story.
A. In 1939 on 30 November, Soviet paratroopers had the distinction of making the first combat jump in history when they dropped at Petsamo and other points behind the Finnish lines during the Soviet invasion of Finland. Due to poor navigation on the part of pilots and quick action on the part of Finnish snipers who picked off many as they landed, few of these paratroopers actually made it into combat. Those who did fought with courage, and many had even jumped without parachutes into deep snow drifts.
B. Soviets experimented experimented with paratroops who jumped from a plane without parachutes. The idea was the plane sould slow down to less than 100 mph, and it was to be done ONLY over large fields covered with deep fluffy snow- about 5 to 6 ft deep.
(Just as a note, having lived in high snow regions, you don't have deep fluffy 5 ft+ snow difts. When snow gets that deep, it starts to pack down and turn to ice. So this would be close to jumping onto concrete. The joke used to be, the snow fell in Oct and the same snow was still on the ground in May - just packed into ice underneath all the rest of the snow.)
C. At the Petsamo drop, Soviet's paras dropped in wooden crates lined with straw and dropped from bombers into deep snow.
At Petsamo, all the paratrooper's were issued parachutes - and records do existed that show this. Further, the reports of no parachutes first surfaced in the late 50s. And when you try to find actually reports of this happening, they just don't seem to exist - or at least, I have never been able to find them.
So as much as this would prove that Russian paratroopers were the true manly men of the airborne, this colorful story seems to be exactly that - a colorful story.