Thomas attended Cavendish and Scotch College in Melbourne, and subsequently entered the University of Aberdeen, after which he embarked on a long tour of Europe and the United States.

Skene married Margaret Scott Anderson on 2 September 1871, and ran Bassett, his father's property near Branxholme, from 1868, where he bred merino sheep.

He sold the property in 1882 to finance a venture in New Mexico; he was unable to come to terms with the Mexican Government, however, necessitating his return to Victoria.

Maintaining a Melbourne home from 1892, Skene served on both the Portland and Stawell shire councils, was a founder of the Chamber of Agriculture, and was president of the Royal Agricultural Society of Victoria 1897–99 and 1906–08, having been a councillor since 1892.

He also held the positions of chairman and president of the Colonial Bank of Australasia and director of the Trustees Executors & Agency Co. Ltd. Skene unsuccessfully ran for the Victorian Legislative Assembly in 1892 for the seat of Dundas.