Initially representing the Division of Northern Territory, and later the Division of Lingiari, his constituents consisted of all the residents of the Northern Territory located outside Darwin, as well as Christmas Island and the Cocos (Keeling) Islands in the Indian Ocean.

He served as Parliamentary Secretary to the Shadow Minister for Regional and Urban Development, Transport and Infrastructure (Northern Australia and the Territories) 2001–04.

Snowdon was sworn in as Minister for Defence Science and Personnel in the first Rudd ministry on 3 December 2007.

[4] Snowdon narrowly retained his seat at the 2013 federal election, largely due to his winning all but five booths.

He sat on the "Inquiry into the destruction of 46,000-year-old caves at the Juukan Gorge in the Pilbara region of Western Australia" from June 2020.