Born in 1912 to a Jewish family in Vienna, Hilda Goldwag's artist father, Moses Leopold Goldwag, died when she was nine, leaving her mother, Szerena, to raise the family of three children.

Goldwag attended art classes for gifted children and, aged 14, was among pupils chosen to paint murals for the new St Leitener Kindergarten.

She gained her degree in Vienna, in 1938, despite the Nazi invasion of Austria, and received a permit to leave Austria, arriving in Scotland in 1939. However, in Vienna her family were forced from their home, and although they were all due to follow her to Scotland, the war broke out and they were trapped in Austria. They were murdered during the Holocaust, in Dachau in 1943.

Goldwag came to Glasgow in 1940 doing war work at McGlashan's engineering works. From 1945 to 1955, she was head designer at Friedlanders in Hillington, designing scarves for Marks & Spencer.

She did freelance illustration work for Collins publishers and, from 1962 to 1975, worked part-time as an occupational therapist at Forresthall Hospital, Springburn.

She initially lived in Hill Street beside Glasgow School of Art, but in 1968 moved to Knightswood where the new low-rise blocks of flats were close to the Forth and Clyde Canal, the subject of many of her paintings. She painted and exhibited from the 1950s, principally working with oils, often capturing tenements and warehouses before they were demolished.

From the 1980s, she exhibited flower pictures, farm landscapes and canal and waterscape paintings, along with figurative paintings.

Following the death of her lifelong friend Cecile Schwarzchild in 1997, she lived alone and carried on painting for a number of years.