The son of a former vicar, Edwin Moulder was educated at Queen's College, in Georgetown, where he won the Guiana Scholarship in 1891, and at Merton College, Oxford. He gained third class honours in History in 1895. He qualified as a Bachelor of Arts in 1896 and served as Assistant Master, Lodge School, Barbados, from 1899 to 1901.
Moulder made his first class debut for Guyana as an opening batsman, against Trinidad, at Bourda in September 1901, top-scoring with 52 in the second innings. He followed this with 64 in the first innings against RA Bennett's XI, in March 1902, and 64 and 94 not out against the same opposition in April 1902, all at Bourda. Moulder then surprisingly disappeared from first class cricket in 1902.
After reappearing in 1905, Moulder had a series of failures and disappeared again in 1906, returning to Oxford, where he obtained a Master's degree in History in 1908. He returned to first class cricket in 1909, but with no success, missed the 1910 season but reappeared in 1911 and was surprisingly selected for the West Indies, in its pre-Test days. After scores of 20, 10, 30 and 10 for the West Indies, he returned to Oxford and obtained a diploma in Education in 1912.
Returning to first class cricket in 1913, Moulder scored a valiant second-innings 104 not out at Bourda, in a vain attempt to save the West Indies, at the age of 38. He retired from cricket in March 1913 after playing one more match for Guyana the following week.
After returning to British Guiana in 1901, Moulder took up the post of Assistant Master, Queen's College, and held it until 1914. He served as Examiner to the Education Department from 1902 to 1914, and acted as Director of Primary Education from May to November, 1914, and from July to November, 1918. He served as an Inspector of Schools from April, 1914.
He acted as Second Master of Queen's College from October to December, 1916, and acted as Censor, in addition to other duties, from August to November, 1917. He was appointed Principal of Queen's College in February, 1920, from which position he retired on pension on January 1, 1929.
As Principal of Queen's College he was regarded by the boys at that time as a caustic wit, but not a strict disciplinarian. He believed in the development of individual personalities, but there is no doubt that he enjoyed the respect and loyalty of the school. To all, both as a boy and master he was known as 'Sheepie'.
At Queen's College, he played Garnett Cup cricket and helped to raise the standard of play. Perhaps his cricket typified his character more than anything else — an unhurried elegance which made the graceful late-cut of which he was so fond, come as a surprise to the spectator, for its power of wrist and keenness of eye.
In 1954, the number of houses at Queen's College was expanded from three to ten and one of the new houses (G House) was named "Moulder House" in honour of Edwin Moulder.