Smith was born on August 6, 1820, in Moray, Scotland. He was the second son of Alexander Smith (1786-1841) and his wife Barbara Stuart, daughter of Donald Stuart of Leanchoil, Upper Strathspey, descended from Murdoch Stewart, 2nd Duke of Albany. His father, whose family had lived at Archiestown Cottage as crofters at Knockando, became a saddler at Forres after trying his hand at farming and soldiering. Donald was also a first cousin of the successful and notably philanthropic Grant brothers of Manchester, who were reputedly immortalised as the "Cheeryble Brothers" in Charles Dickens' book, Nicholas Nickleby. Donald's mother was the sister of the Canadian explorer John Stuart, partner of the North West Company who rose to become Chief Factor of the Hudson's Bay Company.