I'll start with a little background knowledge that I have of Mongolia. Tibetan Buddhism was readily accepted because its tantric nature incorporated many of the traditional shamanistic beliefs. This form of Buddhism took hold and helped "assimilate" Mongolia. By the 17th century Mongolia was incorporated under Chinese rule, having submitted to the Manchus, with whom they still had some common background. As China's last dynasty (Qing) weakened and eventually fell, Mongolia declared its independence.
However, the new Republic of China tried to occupy Mongolia as it had been a part of China for centuries. This is when Baron Ungern (White Russians) intervenes and kicks out the Chinese soldiers. Then the Soviets saw this as an opportunity to expand and in 1924 establish Mongolian People's Republic, effectively redeclaring independence from China.
Then the bad times came, Soviet collectivization of livestock, persecution of Buddhists, and the Stalinist purge(s). Essentially Mongolia was a part of the USSR and treated like any other part, it was defended from Japan during WWII but subject to the whims of the state. Introduction of vodka certainly ruined many.
In more recent times, Mongolia has leaned heavily on the Soviet Union for economic and political support. Most of Mongolia's state debt was written off, and they receive reduced price oil/gas exports.
So to answer your question, the comparison to Warsaw Pact countries is accurate in my opinion. USSR influence was very deep and extensive and continues in this century.
The Changing World of Mongolia's Nomads by Melvyn Goldstein and Cynthia Beall
National Geographic Magazine (I'll add the precise issue given the chance to search my collection)