Army Group South, Fall Blau, and the Stalingrad area of operations including the battle for the city itself is where my knowledge is the strongest, so you're very correct. A very famous Division in Stalingrad, the 13th Guards Division (portrayed in the movie as well as many video games) are seen in pictures with their signature loadout of greatcoats, helmets, PPShs, and a gas mask bag.
Starvation was a large problem for both sides in Stalingrad and the best way to feed the troops were to drop canisters and crates by air, although the amount of anti-aircraft capabilities by both sides were devastatingly huge.
I read a story about German troops in the Red October Factory complex noticing that the Russians holding their narrow strip of land on the banks of the Volga would show where they were by fires and would be dropped supplies. So the Germans did it themselves and received food that way until the Russians caught on.
Speaking of food, if not for the Lend-Lease program, thousands or more Russians would've starved to death during the Winter of '41 up until later in the war. The most recognizable item being... Spam. Yep.