To the extent that petroleum *was* a strategic factor in WWII, researching, I found that about 72% of the Soviet Union's oil would come from Baku. Interestingly, also Stalingrad/Volgograd is at a bend in the Volga river, which leads to the Caspian Sea, where Baku is located.

Even if horses were also food, overall, I think we can conclude that the move on Stalingrad was motivated and demonstrated by the preference for getting petroleum supplies. The terrible cost of defending Stalingrad was justified to the Soviets by the necessity to maintain oil supplies for the long haul.