If the goal of the article was to find who was the first person who referred to himself, or was referred to by others, as a golf architect HS Colt is not the man. Colt did design Rye in 1894 (with Douglas Rolland) but that was an isolated incident. His real career began later as secretary of Sunningdale. He first remodeled that course around 1906, and shortly afterward began dabbling in design consultation, which led to him devoting considerable time to architecture 1907-1911, and his final resignation in 1913. The first mention of architecture in association with Colt (I have found) is a 1909 letter he wrote to the editors of Golf Illustrated during the controversy dealing with 'amateur green architects,' and in that letter he never used the term architect or architecture. The first example I see him using the term was a chapter he wrote in Sutton's Book of The Links, 1912, entitled 'Golf Architecture.'
Ross really didn't become a serious golf architect until around 1910, and that year he gave an interview about modern British golf course development, and 'British architects of golf.'
The term was not used about or by Willie Park until moved to America in 1916. I have found no early use of the term by Braid or Taylor. The first example I have found for William Watson was 1912, in a British magazine ironically. Around that same time HH Barker began advertising himself as a golf architect before that he specialized in laying out new courses.
The first example I have found for Tom Bendelow is 1908, but I suspect he used that term earlier.
In 1907 Herbert Fowler was referred to as the 'popular green architect.'
The first examples I have found for CB Macdonald, Walter Travis and Devereux Emmet is a 1907 article in British Golf Illustrated, describing them as the architects of the new National course. A year later there was an article entitled 'New Ideas in Golf Course Architecture,' written by Travis about Emmet's new Salisbury Links.
Horace Hutchinson first used the term Links Gardner in the 1890s, which later evolved into Linkscape Gardner, and eventually he settled on Course Constructor. The first time I have found him using architect was his autobiography written in 1914.
Speaking of Hutchinson the earliest examples I have found was in his book Golf Greens and Green-keeping (1906), and they are found in couple of chapters written by HH Hilton, one on laying out a course and another on championship courses. Hilton was involved in design, but I think that came later. At this point he was more of a theorist. It is interesting he is the only one to use the term in a book loaded with a who's who of golf architects - Hutchinson, Hutchison, Colt, Fowler, Braid, Lees, and Mure Fergusson.
So based on this quick search, if you disqualify Hilton because he really wasn't a golf architect, the first would be Fowler, Macdonald, Emmet and Travis in 1907.