I don't believe they would actually ride the horses in to battle, most they would be used for: quick movement and mobilization.
so, they could maybe ride to somewhere but they would dismount before battle.
EDIT: direct copy & paste from wikipedia
here it goes.
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During the Second World War Cossacks found themselves on both sides of the conflict once again. While most historians agree that the majority of the Russian Cossacks fought in the ranks of the Red Army, a substantial number of them also served with the Nazis. This can be explained by harsh repressions that many of them suffered under the collectivization and Decossackization policies pursued by Joseph Stalin. Like other peoples of the Soviet Union, who suffered persecution under Stalin, many Cossacks dreaming of autonomy greeted the advancing German army as liberators.
While the core of the Nazi collaborators was made up of former White Army refugees, many rank-and-file Cossacks defected from the Red Army to join the German armed forces (Wehrmacht). As early as 1941, the first Cossack detachments, created out of prisoners of war, defectors and volunteers, were formed under German leadership. The Dubrovski Battalion formed of Don Cossacks in December 1941 was reorganised on July 30, 1942 into the Pavlov Regiment, numbering up to 350 men. The Cossacks were successfully utilized for anti-partisan activity in the rear of the German army.
The Cossack National Movement of Liberation was set in the hope of creating an independent Cossack state, Cossackia. It was not until 1943 that the 1st Cossack Division was formed under the command of General Helmuth von Pannwitz, where Cossack emigrees, like Andrei Shkuro and Pyotr Krasnov, took leading positions. The 2nd Cossack Division under the command of Colonel Hans-Joachim von Schultz, formed in 1944, existed only for a year, as both Cossack divisions were transferred into the Waffen-SS and merged into the XVth SS Cossack Cavalry Corps in 1945. The Corps contained regiments of different Cossack groups: Don, Kuban, Terek and Siberian Cossacks. At the end of the war in 1945, they surrendered to the British Army in Allied-administered Austria, hoping to join the British to fight Communism. There was little sympathy at the time for a group who were seen as Nazi collaborators and who were reported to have committed atrocities against resistance fighters in Eastern Europe. They were accordingly handed over to the Soviet Government. At the end of the war, British commanders repatriated between 40 to 50 thousand Cossacks, including their families, to the Soviet Union. An unknown number were subsequently executed or imprisoned. Reportedly, many of those punished had never been Soviet citizens. This episode is widely known as the Betrayal of the Cossacks.
The majority of the Cossacks fought in the ranks of the Red Army on the Southern theatre of the Eastern Front, where open steppes made them ideal for frontal patrols and logistics. A Cossack detachment marched in Red Square during the Moscow Victory Parade of 1945.
Cossack cruelty and savagery in WWII is legendary. Halina Kahn, a young Polish Jewish woman in the Lodz Ghetto remembers, "We are free, the war is over, the Russian Army is coming in. That was a terrible agony: they were Cossacks and they had been on the front for three or four years, dirty and black, and they saw women for the first time and would take the women and girls to the barracks. They raped these hungry women and left them like little heaps of rubbish."
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So, maybe they could be used as recon units for the ostheer but I doubt.
