Compared to many armies of the time, soviet equipment was relatively simple, which doesn't make it poor by any sense of the imagination. When it comes to 'bedrolls' an average soldier in the RKKA would not have any such thing. Instead, every soldier of the RKKA carried his or her great coat all times of the year, which doubled also as a blanket.
What was done was you'd cozy up to 2+ other members of your unit, and have one greatcoat with the collar facing one way, and the other greatcoat facing the other. This would form a basic square shape to use a proper blanket.
They were also issued a variety of other winter clothing like the ubiquitous ushanka, as well as quilted suits, which were designed to be worn under the greatcoat for extra warmth, but were frequently worn on their own. As well as the rain cape, which could be used as a shelter on its own, or could wrap ones self in making a quasi sleeping bag. While there are instructions in pre/early war RKKA manuals about how to make this 'sleeping bag' out of a rucksack, greatcoat, and rain cape, I have never come across any memoirs of soldiers making one or even being trained how to.
Bunkers would also be frequently dug with stoves, and would be lined with foliage or any large pieces of fabric which could help hold in the heat. Also keep in mind, depending where these soldiers lived before the war, they likely had experience in extreme cold.
This also isn't to say the RKKA didn't have its issues with the cold. Following the Winter War, some new winter clothing (the most iconic being the ushanka replacing the budenovka). And there are also plenty of accounts of Soviet soldiers freezing to death during the winter months.
My sources for this were
Merridale, Catherine. Ivan's War: Life and Death in the Red Army, 1939-1945. Surrey UK: Picador Publishing, 2006.
Rio, Phillipe. Soviet Soldier 1941-1945. Paris: Histoire and Collections, 2011.
Dobroff, Ivan & Mark A. Sevigny. Handbook for Infantrymen of the Workers and Peasants Red Army of the Union of Soviet Socialist Republics. Great Patriotic War Publications, 2008.
Red Army. Infantry Fortification Manual. (Moscow: Military Publishing House of the Ministry of Defence of the USSR, 1953).