Several dictionaries of British artists make the erroneous suggestion that he was probably the son of H B Carter, the Scarborough artist who lived for a time at Torquay. R H Carter was born in Truro, Cornwall (19 March 1839, GRO),  the son of John and Elizabeth Carter and baptised at Truro St Mary's on 24th July 1839. His father was a naval pensioner who had died by 1851 when R H was an apprentice stationer living at Fairmantle Street, Truro with his maternal grandparents, mother and siblings. By 1861 he was a clerk in the copper office and was living in Walsingham Place,Truro.

He painted scenes mainly in Cornwall and Scotland, his earliest recorded works being in 1864. He exhibited at RA and RI from 1864 and at other leading London Galleries. In 1866 he married Ellen Dunn at Truro and they were to have at least three children. 1871 sees him recorded as an accountant and artist living at Strangways Terrace, Truro. He illustrated J T Tregellas' book of 1879 Peeps into the Haunts and Homes .... of Cornwall. In 1881 while still at Strangways Terrace, he is recorded as an artist (landscape) and cashier, while his wife is a professor of music. He was still exhibiting from Truro in 1882 but by 1884 he was living in Falmouth. 

By 1891 he and his wife had moved to London and in that year he held an exhibition entitled 'The Shetland Isles' at Arthur Tooth and Sons Galleries in The Haymarket. By 1894 he was exhibiting from Petersfield, Hampshire. At the 1895 Opening Exhibition at Newlyn he showed watercolours of Cornish coastal scenes. By 1896 he was exhibiting from an address in Plymouth and it would appear that his wife continued to live there as she was still there in 1901 while RH was living as a boarder with a fisherman and his family at Sennen Cove. In his later years he took to painting in oils and did less work in watercolour.

Carter was the fellow artist who set off with Walter LANGLEY in July 1904 for Holland, staying at Volendam on the Zuider Zee. There they joined up, and stayed for almost a month, with a flourishing colony of artists led by two younger members of the Hague School, Willy Sluiter and Albert Newhuys. A group (5) of his representative paintings are in the fine art collection of the Royal Cornwall Museum (RCM) at Truro. He died on 7 February, 1911, at Sennen, Cornwall (GRO) at the age of 71.