With regards to military capabilities, I will say that while a stalemate was achieved between Chinese and U.S. forces in Korea (using a combination of human wave and infiltration tactics), by the time of the ceasefire that stalemate was beginning to show cracks in the face of increasingly glaring logistical and technological deficiencies in the PLA.
That being said, however, the PLA was still in perfectly fit shape to take on both Tibet and Mongolia with one hand tied behind its back.
Beyond that fact, the point still stands that Mongolia was a Soviet sock-puppet at that point in time, and the Soviet's were still plenty friendly enough with the PRC at that juncture that they wouldn't allow Mongolia to mess with affairs of its much larger and more important ally.