As for crossing rivers. I don't actually know how likely that is. The rivers in Ukraine are the good kind that flow North to South which means they don't necessarily freeze up. Rivers in Siberia have the bad habit of flowing South to North which causes all sorts of swampiness when all that river backs up because of ice.
However, having read all that. I see that the Dnipro does often freeze over. Regardless, the Russian Army have bridging equipment.