The vast majority of German soldiers in 1941-42 wore no dedicated camouflage clothing. The standard uniform was a grey-green (feldgrau) blouse and trousers, worn with tall marching boots and a steel helmet, as seen here. Each soldier did possess a camouflage tent quarter which could be worn like a poncho (zeltbahn. And as seen in the photo, rubber tubing or even chickenwire could be worn on the helmet to secure foliage to it. Nor did they wear bright red armbands; only the Allgemeine (civilian) SS wore them with their dress uniforms.

While it's true that the German military invested in camouflage in the subsequent years, only the Waffen SS was able to equip its soldiers with camouflage clothing as a matter of course. The typical German army soldier was still wearing field gray when he surrendered in 1945. This photo is illustrative of the differences in appearance.

It is my understanding that the Soviet snipers only had major success after the initial German conquests, when the war had become a bitter struggle of attrition. This is not surprising: snipers typically excel under such conditions. Additionally, the Soviet sniper program was well developed and supplied trained marksmen (and women) well versed in field craft and sniping doctrine.