In Stalingrad the soviet cavalry was still issued sabres so I guess they used them while mounted on their horse but nothing stopped them from dismounting and then attacking.
Also the italians and Romanians had cavalry units in Stalingrad.
Cavalry would be a bigger target but they would also move very fast.
I wouldnt like it to face them in Spartanoska for sure.
Can you please name an italian cavarly unit in stalingrad? There were only a transport unit in stalingrad afaik, and not on horses for sure.
Cavalry was used in many armies, mostly as a cheap "motorized" brigade. They also had some degree of motorization as the war advanced. The main purpose was to transport the troops somewhat fast around the battlefield, then dismount the horses in a safe location and deploy the squad as infantry, often with less support units (think light artillery, mortars, mgs, some were horse towed but...) Consider also that horses requires a lot of care to be at top (irons, food, medical care, furnitures like saddles and garnments, and a lot of things that your regular infantry battalion doesn't need...) and the eastern front wasn't exactly friendly on supply routes. Also, horses have the bad habit to die or be incapacitated by enemy bullets, shrapnel, and such (bad horses, baaaad ) and reserves weren't huge and right behind the corner (at least, not for the italians, that's for sure)
Charging on horse with sabres and grenades may sounds cool, but would require TONS of work to code, animate, and escpecially, fit on the map and terrain on a realistic way. Not really worth it.
Also, cavarly charges were VERY outdated by the time, and could only work in especially good conditions for the attacker, like night\fog and against poor armed foes (also read few machineguns\mortars) But i recognize some cavalry charges were effectively made (one quite famous by italians, can't rem the name right now)
All in all, definitely not in stalingrad rubble, frosted, streets. They would be simply too easy to kill\incapacitate.