Snetkov was born on 27 February 1925 in Saratov, and graduated from Pugachyov's School No. 2. He was drafted into the Red Army in 1942 and in October 1943 graduated from accelerated courses at the 2nd Kiev Self-Propelled Artillery School as a junior lieutenant. As commander of an SU-152 self-propelled gun in the 9th Separate Guards Breakthrough Tank Regiment of the 1st Ukrainian Front's 38th Army, Snetkov saw his first combat west of Rozhiv in the Battle of Kiev on 25 November, during which his crew was reported by a superior to have destroyed a Tiger tank and two guns. For his actions, Snetkov received the Order of the Red Star on 12 December. As the advance westwards across Ukraine continued into the winter, he and his regiment fought in the Zhitomir–Berdichev Offensive and the Korsun-Shevchenkovsky Offensive as part of the 38th Army. During the latter operation, on 26 January, his crew was reported by a superior to have engaged a German tank column of about 20 tanks and destroyed three, one of which was a Tiger, on the LipovetsRososhe road. For this action, Snetkov received the Order of the Patriotic War, 1st class, on 2 February.