In the early 1940s, she moved to New York City to join the ballet corps at Radio City Music Hall. From 1945 to 1947, she was a member of the American Ballet Theatre; she joined the New York City Ballet shortly after its founding in 1948. She performed there many times with noted Dancer Jacques d'Amboise. From 1955 until her retirement in 1973, Hayden was the prima ballerina of the New York City Ballet.
Hayden appeared frequently on television, especially The Kate Smith Show and The Ed Sullivan Show. In 1952 she performed as the dance double for Claire Bloom in the film Limelight.
Hayden married lawyer-businessman Donald Coleman. The couple had two children, Stuart (b. 1954) and Jennifer (b. 1961). Hayden died at her home in Winston-Salem of pancreatic cancer, aged 83.
In 1965, she was seen on American TV as the Sugar Plum Fairy in a one-hour German-American adaptation of The Nutcracker. Filmed in 1964, and first shown in the United States by CBS just four days before Christmas 1965, the production, with a heavily altered storyline, featured an international cast of Dancers and English narration by Eddie Albert, who was at the time in the first year of the run of Green Acres. Edward Villella and Patricia McBride also starred.
After appearing in over 60 ballets, mainly works by George Balanchine, Hayden retired as a Dancer in 1973. Balanchine honored her on her retirement by creating the ballet "Cortege Hongrois", which is still part of the New York City Ballet's repertoire. At the premiere of the piece, Mayor John Lindsay presented Hayden with the city's Handel Medallion, praising her as an "extraordinary ballerina who has filled the hearts of her audience with joy."
After her retirement, she became head of the ballet department at Skidmore College, and taught ballet at the School of Pacific North West Ballet in Seattle, and in New York City, where she opened her own school. From 1983 until just a month before her death, she taught at the North Carolina School of the Arts in Winston-Salem, where she stressed and impressed upon the student body the importance of the Balanchine technique with which she was most famously associated. She rehearsed and staged some of Balanchine's most demanding works including Concerto Barocco, and the masterful Theme & Variations.