Horton was born in the Princeton community of Jackson County, Alabama, one of twelve children of Henry Hollis Horton, a Baptist minister, and Anne (Moore) Horton. He attended Scottsboro Academy in Scottsboro, Alabama, before graduating from Winchester College in Winchester, Tennessee, in 1888. He moved to Hillsboro, Texas, to teach school, but returned to Tennessee after about a year. He attended the University of the South in Sewanee in the early 1890s.
Horton was admitted to the bar in 1894, and practiced law in Franklin County. He held various local offices, including school director and election commissioner, and worked as director of the Home Bank of Winchester. He represented Franklin County for one term in the Tennessee House of Representatives, from 1907 to 1909. He was a supporter of prohibition.
In 1911, Horton moved to Marshall County, Tennessee, where he operated a farm and mill that had been established by his in-laws, the Wilhoites, on the Duck River near Chapel Hill.
Horton was elected to the Tennessee Senate in 1926 for the district of Marshall and Lincoln counties. When the senate convened early the following year, he was chosen as Speaker of that body, which in Tennessee is the governor's constitutional successor. Following Governor Austin Peay's death on October 2, 1927, Horton thus became governor.
Unfamiliar with running a statewide campaign, Horton turned to Peay's old advisor, Nashville Tennessean publisher Luke Lea, to help him win reelection in 1928. Lea's rivals, Memphis political boss E. H. Crump and Nashville political boss Hilary Howse, both endorsed Hill McAlister, who had been defeated by Peay in 1926. A third candidate, Lewis S. Pope, also sought the nomination, and had the backing of Peay's widow. After a hard-fought primary campaign, Horton won the nomination with 97,333 votes to 92,017 for McAlister, and 27,779 for Pope. In the general election, he defeated the Republican candidate, Raleigh Hopkins, 195,546 votes to 124,733.
During Horton's second term, he and Lea began using state patronage in Memphis in an attempt to weaken Crump's influence. Crump, who was running for Congress and wanted to focus on his own campaign, agreed to support Horton in the 1930 governor's race if he and Lea would stop providing patronage to his foes. With Crump out of the way, Horton defeated his chief opponent, L. E. Gwinn, 123,642 to 88,416 in the primary. He then defeated the Republican candidate, C. Arthur Bruce, in the general election, winning 144,995 votes to Bruce's 101,285.
While the stock market had crashed in 1929, its effects had not fully reached Tennessee by the 1930 elections. Just four days after Horton was reelected governor, however, the Bank of Tennessee, which was controlled by Lea and his business associate, Rogers Caldwell, was declared insolvent, and numerous banks controlled by Caldwell across the South soon followed. Horton had deposited over $6 million (the equivalent of over $86 million in 2017) in state funds in Caldwell's banks, all of which was lost.
Crump and his allies, sensing an opportunity, assailed Horton for depositing state funds in the banks of his political allies. They also attacked Horton for awarding no-bid contracts to Caldwell's road-paving company, Kyrock. A motion calling for Horton's impeachment was voted on by the state House in June 1931, but the motion failed, 58 to 41. Horton was allowed to finish out his term, but did not seek further reelection, which would have been permissible under the term limit provision in the Tennessee State Constitution at the time, which limited an incumbent to three consecutive full two-year terms. However, both Lea and Caldwell were eventually convicted of bank fraud.
During Horton's tenure as governor, he continued most of Peay's reform initiatives. He abolished a land tax that had been unpopular with farmers, established a parole board, created a state division of aeronautics, and developed a secondary state highway system. He also had statues of Andrew Jackson and John Sevier placed in Statuary Hall in Washington, D.C.
Following his final term as governor, Horton retired to his farm in Marshall County, where he died from an apparent stroke on July 2, 1934. He was buried in Wilhoite Cemetery in Chapel Hill.
In 1961, the state purchased Horton's Marshall County farm from his heirs, and subsequently redeveloped the land as Henry Horton State Park. The park is still home to the ruins of a mill operated by Horton and his in-laws, the Wilhoites.
Along with the state park, a portion of U.S. Route 31 in Marshall County has been named in Horton's honor.
Horton married Adeline Wilhoite in 1896. They had one son.