Horgan was educated in the School of Physic, Trinity College, Dublin, qualifying in 1933. He then came to England and was, successively, a house surgeon at Bristol Royal Infirmary, and resident surgical officer at Bolton Royal Infirmary and at Brighton Municipal Hospital. He took the English Fellowship in 1938, but returning to Ireland held a resident position at the Rotunda Hospital, Dublin, and then practised for nearly thirty years at Tralee, Co Kerry, where he was surgeon to the County Infirmary, later removing to Waterloo Road, Dublin, where he died early in 1969. His wife Jane died at Micheldever, Hampshire on 23 October 1973. Horgan had been a Fellow of the Royal Irish Academy of Medicine.