Russia, while it was assisted by the United States, still managed to hold off over 3.8 million axis troops from Moscow and Stalingrad. besides, they were better in winter anyways, the United States supplying tanks on the eastern front wouldn't matter, the axis would have most definitely lost either way.
Russia's main goal was to send people into space, but not to put them on the moon due to a failure in one of their shuttles, so they didn't even try. IF they did, they would most likely do it before the United States due to their lead over them in the Space Race.