Born near Norwich in 1833, Boughton was taken to America when his parents emigrated the following year but returned to settle in England in 1862. He began to exhibit at the Royal Academy in 1863 and also showed at the British Institution and the Grosvenor and New Galleries. The present picture, which, in common with much of Boughton's work, does not seem to have been exhibited, takes its subject from the early history of New York, when the city was a small but rapidly expanding Dutch settlement established at the south end of Manhattan Island by the West India Company. Its name was changed from New Amsterdam to New York in 1664 when it surrendered to an English fleet sent by the Duke of York to conquer the province of New Netherland. The picture is characteristic in being both a snow scene and a New England subject. Boughton scored his first success with a picture entitled Winter Twilight which he exhibited at the New York Academy of Design in 1858, and many of his subsequent figure subjects had winter settings. The first of his numerous New England subjects - Early Puritans Themselves from Indians and Wild Beasts - was exhibited at the Royal Academy in 1867.

New Year's Day, New Amsterdam dates from the period in Boughton's career when his pictures made a great impression on Van Gogh, who mentions them in several letters written during his stay in England in the 1870s; they were not only seen by him at exhibitions but handled by Goupil's, the dealers for whom he worked (see English Influences on Van Gogh, exh. organised by the Fine Art Department, University of Nottingham, and Arts Council, 1974-5, cat. pp. 13-20). Another admirer was Henry James who often praised Boughton in his art criticism (see John L. Sweeney (ed.), The Painter's Eye, 1956, passim). The two men belonged to a circle of expatriate Americans which also included E.A. Abbey, John Singer Sargent and Frank Millet.

Boughton's studio sale was held at Christie's on 15 June 1908.