What appeared to be winning the Korean War until China actively entered the conflict?
By what i'm guessing you mean who and by what tactic. The western powers (who were helping the south koreans) were winning the war prior to the Chinese entering. This is because they had strong belief in the policy of containment- though up by George Kennan, which said that wherever communism was spreading, the USA would be there to stop it. There was then a vote in the United Nations as to whether other countries should go in. This vote passed and over 25 countries sent troops in, which made the North Koreans retreat up to the Yalu river, near China.
Until substantial ground forces of Communist China entered the conflict in 1951, the Korean War was in fact being won by the associated American, international (or, United Nation), and (South) Korean troops arrayed against their North Korean enemy. With the entry of China, fortunes reversed several times for each side before a shaky truce was arranged in 1953.