Any radio sitcom that lasts more than one season is likely going to do a Christmas Radio Shows. I think it may be an FCC rule. It is fun to think about, especially for pre-recorded TV Sitcoms that are probably shot the previous summer.
The Grand daddy of all radio sitcoms, Fibber McGee and Molly had many wonderful Christmas Radio Shows over their 24 year run. Many shows seem to be OK with just one nod to the holidays every season, but Fibber McGee and Molly had many years where they had a Christmas themed radio show most weeks in December. Whether this is because stars Jim and Marian Jordan were an actual couple raising kids who would have wanted more Christmas cheer, or if writer Don Quinn was just a big kid at heart is purely up for guess. Maybe Harlow Wilcox and the Johnson Wax company had a Santa Complex.
On Dec 10, 1940, Fibber McGee and Molly try to mail their Christmas packages, not only do they have to deal with long lines at the post office, but Fibber is talked into mailing Gildersleeve’s packages as well. Then they find out Fibber has stood them in the wrong line at the post office!