Notes on that page say that the author's sister was married to a well-known storyteller Donnchadh Dòmhnallach. When Donnchadh came from Uist to Glasgow to take part in a BBC radio programme he stayed with Dòmhnall Mac an t-Saoir, aka "Dòmhnall Ruadh mac Aonghais Ruaidh", and his wife Màiri NicIllFhialain. During this time, Donnchadh generally wore a red or (more likely) russet-coloured Harris tweed coat, which is commemorated in the song.
Donald Joseph MacKinnon would be Dòmhnall Eòsaph MacFhionghain, so according to the BBC site "Bliadhna nan Òrain", Donald MacKinnon is the singer but not the author. The site says the author is Dòmhnall Mac an t-Saoir . Mac an t-Saoir could be Anglicised as MacAteer. Dòmhnall Mac an t-Saoir also wrote the lyrics of Óran na Cloiche