As a youth, he emigrated to Halifax in Nova Scotia, Canada, to join a brother. Together, they went to Victoria, Australia and joined the Victorian gold rush. He came to Blenheim in the late 1850s and set up a brewery in that town.
In the provincial council, he was the head of the Blenheim party for many years, and they quarrelled against the Picton party.
He was Mayor of Blenheim for four one-year terms (1870–1871 and 1883–1884). He represented the Wairau electorate from 1881 to 1890, when he retired.
In 1881, he beat the incumbent, Arthur Seymour. He was challenged by Joseph Ward in 1884.
In the 1887 election, he was challenged by a former Mayor of Blenheim, George Henderson, and Sutherland John Macalister.
He died on 8 May 1892 at his home in Blenheim, New Zealand after a sudden illness and was survived by seven children.
Dodson was a member of the Marlborough Provincial Council for three different electorates from 1860–1863, 1866–1870, and 1874–1875.