The event will be held on November 17.
The Playwrights Horizons production is directed by Rebecca Taichman.
Justin Sayre will host the event.
Barnhart will take on the roles of a Bad Idea Bear and Mrs. T.
Disney Theatrical Productions will bring the classic novel and screenplay to life onstage.
Rosen will take over the role of Smee from Kevin Del Aguila for the show's final performances.
The event is presented in association with Merkin Concert Hall's Broadway Close-Up Series.
Performers from the award-winning summer theater will offer a winter cabaret series.
Honorees will include Nina Tassler, Linda Lowy, and Michael J. Fox
The one-night-only evening is presented by The Acting Company.