I found out about George Winsor and Mary Cole being the parents, because of a death listing for Robert's brother Charles.
George Winsor and Mary Cole are listed as the parents by the researchers/transcribers of the parish records.
Here is the excerpt I found for Charles Winsor brother of Robert:
Charles WINSOR d Jan 25 1893 Tilt Cove senility 73 years Meth planter Tilt Cove Tilt Cove NOTES: Son of George WINSOR of the West Country, England, and Mary COLE(S) of Conception Bay; per headstone, born June 26 1820 - died Jan 26 1893; husband of Elizabeth MACKEY.
You can find that information for yourself here:
http://ngb.chebucto.org/Vstats/civil-reg-death-1892-93-tw.sh...I hope this helps you some :)