There were parts of Stalingrad on the Eastern side, although very little relative to German control. Crossing the river at the time would have been near suicidal. The Soviets and Germans had destroyed most of the Bridges, and crossing on ice or through freezing water in the winter, while under constant enemy fire, would be a nightmare to say the least. German supplies were not enough either to justify the action, and the Soviets would undoubtedly take advantage of the already depleted force.