Appearances by Daddy Snuffle have been fleeting over the years, his presence usually referenced in dialogue rather than showing up on screen. Like many youngsters who proudly describe their parents, Snuffy has occasionally exaggerated his father's size, such as in Episode 0323 when he claims that his father is twice as big as he is.
When Big Bird calls Snuffy in Episode 1966 (1984) to invite him to view the sunrise with his friends on the roof of 123 Sesame Street, it's early enough in the morning that the Snuffleupagus family is still sleeping, prompting an angry response from the man of the cave who answered the phone at 5am.
Snuffy shows off his baby book and some home videos of when he was learning how to walk in Episode 2267 (1987), both of which he says were made by his mommy and daddy.
In Episode 2747 (1990), Snuffy says that his mom and dad love to give grown-up Snuffleupagus parties all the time, and they're mostly about emptying and filling. Snuffy flashes back to scenes where his mother serves cabbage juice and cabbages, which are consumed by two off-screen snuffles.
In 1992, the producers of Sesame Street tested an episode called "Snuffy's Parents Get a Divorce". After a series of arguments, Daddy Snuffle moved out of the cave, and Snuffy and Alice had to deal with the emotional fallout of a breakup. The episode didn't test well with children, and the producers decided to shelve it.