Mudry was born on 19 March 1893 in the village of Okno in Skalat District, Kingdom of Galicia and Lodomeria, Austria-Hungary (today Vikno in Chortkiv Raion, Ukraine).

In 1935 UNDO experienced an internal conflict due to its policy of cooperation with the Polish government.

This pro-German approach ended when Germany's ally Hungary conquered Carpatho-Ukraine and the Polish government renewed its stated commitment to Ukrainian autonomy.

[1] When Germany invaded Poland in 1939, UNDO under Mudry declared its loyalty to the Polish state.

[2] Fleeing the Soviets who annexed Eastern Poland and who arrested most of the Ukrainian political figures who had not escaped (including Mudry's predecessor Dmytro Levytsky), Vasyl Mudry settled in Kraków where he became secretary of the Ukrainian National Committee.