His uncle, Franc Snoj, was a prominent member of the Slovene People's Party and a minister in the Royal Yugoslav Government.

Together with Dane Zajc, Gregor Strniša, Dominik Smole, Marjan Rožanc, and others, he was part of the generation which, influenced by the "modernist turn" of the poet Edvard Kocbek, strongly challenged the literary canon established by the Communist regime.

In 1963 he published his first collection of poetry, Mlin stooki ("The Mill with Hundred Eyes"), which was strongly criticised by the literary establishment for its supposedly decadent and nihilist content.

Snoj later moved closer to Catholicism, expressing religious and metaphysical preoccupations in works as Žalostinka za očetom in očetnjavo ("Elegy for Father and Fatherland") and Duhovne pesmi ("Spiritual Poems").

Among his novels, the most famous are Gavženhrib ("Gallows Hill"), an autobiographical novel about his war childhood, in which he explores the sources of evil, and Jožef ali zgodnje odkrivanje srčnega raka ("Joseph or the Early Diagnosis of Heart Cancer"), in which he placed the ancient archetypal figure of Joseph in a magical realist setting, in which modern and archaic intermingle.