Horner's family moved to Sydney in 1930 where he completed school and trained at Sydney's National Art School. While studying, he acted in radio drama and worked for Smith's Weekly, The Bulletin and the ABC Weekly.

From 1940 he served in the armed forces. After the Second World War, he travelled and worked in Europe. He attended the Central School for Arts and Crafts in London and worked for magazines such as Tribune, New Statesman and Punch.

Horner is most known for his comic strip, Colonel Pewter, created for the News Chronicle in 1952. He was the sole writer and artist until 1970, with a brief revival in 1977. The strip was published in Australia in Melbourne's Age.

Horner returned to Australia in 1976, working mainly for The Age, as well as doing book illustrations and other cartooning. For The Age, he created the satirical strips, The Uriel Report (1978 to 1979) and Dig: A Graphic History of Terra Australis Incognita (1980).