Starting with 921 acres (3.73 km2) purchased from his family, Robert Alexander built his Woodburn Stud at Spring Station, Kentucky into the leading horse breeding operation in the United States.

He also founded Airdrie, Kentucky in 1855 to mine for iron ore, a project he shortly abandoned and returned to his stud farm.

[3] Alexander purchased two African-American enslaved people, Ansel Williamson and Edward D. Brown, who were taught the business of breeding and training horses.

Each went on to train Kentucky Derby winners and had outstanding careers that led to Brown's 1984 induction into the National Museum of Racing and Hall of Fame and Williamson's in 1998.

[4] Alexander is portrayed in the best selling novel Horse by Geraldine Brooks, published in 2022, which is based upon the life of the racehorse Lexington.