I think you base your question on a common misconception. There were no specific "Siberian" divisions in the Soviet Union at the time.

The Soviets had their strategic reserve in southwestern Siberia, at Kazan, and that was where they raised new divisions to replace the ones lost to the Germans. At the crucial time of the Battle of Moscow, the Soviets moved these divisions, plus a few from their Far East Army to reinforce the troops at Moscow. These were compared to the very worn and depleted divisions that had fought the Germans in front of Moscow since early October well equipped, well trained and well supplied - the latter part was an increasingly stark contrast both to the depleted Soviet defenders and the equally (if not more so) depleted German forces.

The elite of the Red Army was rather the Guards divisions - a title any division that distinguished itself on the battlefield could acquire, which allowed for higher pay and usually priority for replacements, new equipment and supplies - but also the toughest jobs on the frontline, spearheading assaults.

The 13. Guards Division at Stalingrad in September 1942 crossed the Volga river in daylight (other transports were usually undertaken in darkness to protect the supplies and troops being moved from German air attack) and assaulted German positions they had captured previously and that allowed them to take the river fleet of barges, tugboats, ferriets etc. under direct fire. The division took 80% casualties in the fighting, but retook the positions taken by the Germans and secured the river supply route, enabling the Soviets to keep fighting in Stalingrad.