Caroline Harriet Hudson was born at Wanlip Hall in Leicestershire, England, and baptised at Wanlip on 1 July 1809. She was the daughter of Harriet Pepperell and her husband, Charles Thomas Hudson, who changed his name to Palmer in 1813 by sign-manual. Caroline lived at home with her family; much of the time she and her two elder sisters nursed their invalid mother. Bemoaning her fate, she wrote, 'No advantage that I can see comes of my living on, excepting that one becomes less and less of a "young lady" every year.' When her mother died early in 1848, Caroline's life began to alter course dramatically. Her considerable artistic talent flourished, and she was able to turn her strong sense of duty and social commitment to better account, especially in the nursing and care of the poor.
On 17 January 1850 in the parish church of Wanlip, Caroline Palmer married Charles John Abraham. Shortly afterwards they travelled to New Zealand, arriving in Auckland on 6 August. Charles Abraham had left his chaplaincy at Eton College to work at St John's College, Auckland, with his old friend Bishop G. A. Selwyn. In addition to this friendship there were family ties which smoothed Caroline's way; she and Sarah Selwyn were cousins. Charles Abraham became chaplain and principal at St John's College and in 1857 the Abrahams' only child, Charles, was born. As an adult he, too, entered the ministry and became a bishop.
During the 20 years she spent in New Zealand Caroline Abraham demonstrated her talent as a watercolourist and recorder, through detailed sketches of the new colony. The extensive panorama of St John's College, Tāmaki, is one of the earliest examples of her work. It was drawn about 1851 and was lithographed by one of the two sisters of W. C. Cotton, a tutor at the college. The bishop's house, the printing office, hall, kitchen, weaving room, surgery and other functional areas of the college are clearly titled. Less didactic are the lively watercolours of Auckland, views of North Head, Howick and Taurarua (Judges Bay), which Caroline painted in the 1850s. In 1857 she and her husband visited England, where he was consecrated bishop of Wellington, in September 1858. They returned to Auckland in March 1859 and in April moved to Wellington. Caroline resumed her sketching, her work now depicting Porirua Harbour and other areas in the Wellington district.
As the wife of an Anglican bishop Caroline Abraham enjoyed a high standing in the community and was involved in issues crucial to the time. She, with her husband, the Selwyns, and Sir William and Lady Martin, prepared a 106 page book on the position of the Māori people, Extracts of letters from New Zealand on the war question (1861). It was printed in London for private circulation. She wrote, 'the people are outspoken and honest and they will not be trodden underfoot and have their lands taken without a struggle.'
In June 1870 Charles Abraham resigned the see to become coadjutor to Selwyn at Lichfield, England. Caroline Abraham died at Bournemouth on 17 June 1877.
A collection of her watercolours, most painted before 1858, is held in the Auckland City Art Gallery. One of the artist's sketchbooks is in the Auckland Public Library; several of the sketches are annotated as being copies of the work of Albin Martin and J. B. C. Hoyte. Other works by Caroline Abraham are held by the Alexander Turnbull Library in Wellington.