Frost was an astronomical assistant at the Harvard College Observatory from 1896 to 1908, under the directorship of Edward Charles Pickering. From 1902 to 1905 he worked at the Arequipa station in Peru using the 24-inch f/5.6 Bruce photographic refractor, made by Alvan Clark & Sons and completed in 1893. His observations of nebulae (following DeLisle Stewart) using four-hour plates were published in the Harvard
60, 179 (1908). He discovered 454 new objects, included in the IC II (Second Index Catalogue of Nebulae Foundation in the Years 1895 to 1907. With Notes and Corrections to the New General Catalogue and to the Index Catalogue for 1888 to 1894, Member Roy Astron Social, Volume(s) 59, Participant 2, p 105, 1908). When moving the Bruce telescope to Boyden station in Bloemfontein, South Africa in 1926, Harvard offered him a job, but he did not go.
Instead he started a dairy farm in Tingo, Peru.
He later returned to Fort Worth, Texas, to work for an oil company doing accounting.
Later still he moved to Shreveport, Louisiana. He is buried in the Forest Park Cemetery at Shreveport, Louisiana.