Hello there!

What you are looking at is in fact a cloak-tent. Official use can be traced all the way back to 1882 when it was strictly used as a tent. However, in 1910, the tent was modernized and renamed a soldier's cloak-tent when soldiers started using them to hide from the rain on a march. This cloak-tent was a light-grey folded-up tent, tied to the soldier's folded up overcoat and worn over his left shoulder. It came with tent poles (cannot see from the photos) which were carried between the overcoat and the cloth.

Today, those who try to wear one quickly discover that it doesn't even reach your knees in the front and a heavy rainfall will soak the feet on a motionless soldier. The cloth was simply a very thin tent that was not even waterproof. A soldier would've become soaked in about 2 hours and provided a surprisingly small number of benefits.

It is a greatcoat roll, since Russian/Soviet soldiers weren't usually issued blankets - the greatcoat would double as such. The standard way to carry it when not being worn was to roll it up as you see there, and sling it around the shoulder with the ends stuck into his mess tin, like here. Sometimes you'll see it on the back in an upside down "U" shape wrapped around his backpack, like here. The soldier also would often have a waterproofed canvas cape (plashch-palatka), which could be wrapped around the greatcoat, or wrapped on its own if the greatcoat was being worn.

Thats about the sum of it.