Winkleman joined the National Youth Theatre of Great Britain in 1997. Winkleman's numerous roles while at Cambridge University included the Bride in Lorca's Blood Wedding, which toured the amphitheatres of Greece, Elizabeth in Six Degrees of Separation, which played at the Edinburgh Festival, Abigail in Arthur Miller's The Crucible, Dockdaisy in Bertolt Brecht's The Resistible Rise of Arturo Ui, Kate in Alan Ayckbourn's Confusions, Madame de Merteuil in Christopher Hampton's Les Liaisons Dangereuses and Fraulein Kost in Kander and Ebb's Cabaret all at the ADC. Winkleman's stage career after Cambridge includes a season at the Royal Shakespeare Company, where she played Veronique in Laurence Boswell's adaptation of Beauty and the Beast and a summer in Bath with the Peter Hall Company playing a variety of roles including Archangela in Gallileo's Daughter directed by Peter Hall, a new play by Timberlake Wertenbaker, Violet in George Bernard Shaw's Man and Superman directed by Peter Hall, and Charlotte in Molière's Don Juan, directed by Thea Sharrock. In 2012 she played Helena in Eric Idle's musical What About Dick at the Orpheum Theatre in downtown Los Angeles, alongside Eddie Izzard, Russell Brand and Billy Connolly.