Nico Kaufmann studied with Vladimir Horowitz in 1937–1939 and is described as Horowitz's only pupil from his European period. Horowitz is stated to have had seven students from 1937 to 1962, including Kaufmann, who was his only student during his time in Europe.
Kaufmann studied piano and composition at the Zurich Conservatory with Emil Frey before taking lessons with Horowitz.