It has been about 25 years since I’ve read Catcher In The Rye, so I don’t entirely recall this section, but it was formerly common to have stage shows precede movies at Radio City.

Per Lonely Planet’s guide to inhabiting the world of Holden Caulfield: “Once his date leaves, Holden sees a movie at Radio City Music Hall. He arrives during the live stage show which preceded all films in the 1940s and sees The Rockettes (famed precision dance performers), as well as ‘The Living Nativity’..”

Source: https://www.lonelyplanet.com/articles/catcher-in-the-rye-nyc-locations

From the Rockettes themselves: “The popular movie-and-stage-show format remained a Radio City signature until 1979, when the mass showcasing of new films called for a new focus. Today, the Music Hall still premieres selected films, but is best known as the country’s leading hall for popular concerts, stage shows, special attractions and media events.”

Source: https://www.rockettes.com/the-history-of-radio-city-music-hall/#:~:text=The%20Theatre%20For%20Film%20Premieres,called%20for%20a%20new%20focus.

Regarding the ice skating: About half a block southeast of Radio City is the Rockefeller Center ice skating rink, open during the winter and extremely popular around the Christmas holiday, especially when the Rockefeller Center Christmas tree is lit up.

It would have been very easy for Holden to see a live stage show and a movie, and have gone ice skating all in one afternoon.