Based on a novel by Attila Orbok, an incognito prince falls in love with an ice skater while rumors fly the prince is romancing her.
At a ski-resort hotel an all-women orchestra plays "My Secret Love Affair." Lili Heiser (Sonja Henie) asks the manager Krantz (Melville Cooper) to let her perform skating; but there is no snow nor guests yet. Nottingham (Arthur Treacher) calls for 84 rooms, and Krantz says they have snow. Krantz, Lili, and her uncle Dornik (Raymond Walburn) pray for snow that comes. Prince Rudolph (Tyrone Power) arrives in a wheel-chair to delay negotiations; but he sneaks out to go skiing. Lili practices ice skating and is seen getting out of Rudolph's car her uncle's cousin drives. People assume a romance with Rudolf. Lili meets Rudolph skiing, and he shares coffee with her. Krantz offers Lili a contract skating, and her uncle Dornik tells her boy-friend Alex (George Givot) to stay away. Reporters flock around Lili. Rudolph's servant Nottingham resigns because of the rumor, but Rudolph says it is not true.
The orchestra leader (Joan Davis) sings "I'm Olga from the Volga." In a disguise Rudolph attends the skating show. Lili and Rudolph ski together. He asks her about the prince and tells her the rumor. The Count (Maurice Cass) and the Baron (Alan Hale) ask Lili to influence Rudolph, and the Baron gives Dornik 300,000. Lili calls on Rudolph, who advises her to go on pretending. People are turned away at the hotel, and Dornik tells how they met in Capri. The orchestra leader sings "My Swiss Hilly Billy." Couples and Lili skate to Strauss waltzes, and the Baron gives Lili a pearl necklace. Nottingham brings Rudolph an angry telegram from Prime Minister Ulrich (Sig Ruman). Rudolph and Lili ski to a cabin and dine. By a fire he kisses her. They ski back and talk of marriage. Ulrich arrives, ordering Rudolph to leave with him. Rudolph says he is getting married, but Ulrich has guards carry off Rudolph. Dornik tells Lili to marry Prince Rudolph; she says she doesn't know him but is engaged to Rudy Miller. The Count tells the Baron that Rudolph has played them against each other, and they unite against Ulrich. Rudolph tells Ulrich that the story is true, and he must marry Lili. Nottingham takes Lili to Rudolph, and she embraces him, causing the Baron to blame the Count. Lili asks Rudolph what she should tell the Prince. Rudolph goes out and comes back as the Prince in the disguise, scolding her until she realizes he is Rudy; then she faints. In the final scene Lili skates.
This musical comedy reflects interest in ice skating and satirizes the aristocratic ways of European diplomacy.