Alistair, is your main objective at present to procure the marriage certificate? Or is getting the marriage record simply a means to an end--that is, to get specific information about where and when Winifred was born, parents' or siblings' names, etc.?
The Minnesota Marriage Index doesn't include the marriage you indicate between Winifred and James, even when I search on date only or bride only or groom only or surnames only. You can try it yourself at:http://www.mncounty.com/Modules/Certificates/Marriage/Defaul...
I see that the England & Wales Death Index indicates a circa 1878 birth year for Winifred H.G. Gordon. Do you already have her death certificate to see if it makes reference to her birthdate, birthplace, &/or mother's name? This might help track her down in a census or other record.
Does the document you have specify that EDWARDS is Winifred's MAIDEN name, or might she have been married to someone named EDWARDS prior to her marriage to Mr. GORDON?
Did Winifred and James have any children? If so, the children's birth certificates might make reference to the mother's birthplace, which might be helpful in tracking down the marriage record you seek.