Alice studied art at the University of Deseret, the Art Institute of Chicago, and privately under George M. Ottingher, J. T. Harwood, John Hafen, Herman Haag, Mary Teasdel, and Henry Taggart. She became closely associated with almost all the prominent Intermountain artists. Lee Greene Richards dedicated a portrait of Bathsheba Smith to "Mother Horne," the name by which Alice was fondly referred to by the artists.

In 1891, only twenty-three years old, Alice was appointed chairman of the Utah Liberal Arts Committee for 1893 Columbian Exposition in Chicago, for which she published a book of poems written by women poets of Utah. She also supervised the preparation of various creations of Utah women that were exhibited in the Woman's Building in Chicago.

In 1898 Alice was elected a member of the Utah House of Representatives, the second woman to serve in that body. She introduced and shepherded through a bill for the state to create an art institute--a landmark bill, as it inaugurated the first art institute in the United States--to encourage the fine arts (art, music, literature, and dance) in Utah; to hold an annual art exhibition, and to initiate a state-owned art collection. In her honor the state collection is called the Alice Art Collection. Mrs. Horne also sponsored a law that provided four-year, tuition-paid teaching scholarships to students at the University of Utah; and she served as chair of the University Land Site committee that chose the present location of the University of Utah.