This scene was ad lib, with Bing Crosby and Danny Kaye reprising the song from Rosemary Clooney and Vera Ellen. It started as Bing goofing around and everyone thought it was funny so they filmed it. They filmed it several times because people were laughing so much that it was hard to get a clean take. The laughter you see here is genuine.
The Queen Of The World and I was watching this, and she found this at 35 surprising "White Christmas" facts.