Like his brother, he was educated at Kingston College in Hull. He was associated with Charles throughout his life, and became the head of the business after his brother's death in 1907. Before this, he served as director of the North Eastern Railway, and chairman of the shipping committee of the Hull Chamber of Commerce. He was High Sheriff of Yorkshire for 1891.
Arthur Wilson is best remembered for playing host, at Tranby Croft in 1890, to Albert Edward, Prince of Wales. During the Prince's stay, one of the party, William Gordon-Cumming, was accused of cheating at the game of baccarat. Baccarat was widely popular in England at the time, but had recently been declared illegal. Several members of Wilson's household at Tranby Croft claimed to have independently witnessed Gordon-Cumming cheating at the game, and after this was brought to the attention of the Prince, Gordon-Cumming signed a document promising never to play cards in the future. This event remained secret for a time, but was inevitably revealed to the press in early 1891. As a result, Gordon-Cumming brought his accusers, including Wilson, to trial on the charge of defamation.[2]
Gordon-Cumming lost the court case, but it brought the Prince much bad publicity, and he never returned to Tranby Croft.