The words “ice box” hint at the age of this recipe. Examples of this recipe show up in newspapers as early as 1924 (which I won’t link because they’re pay-per-view so to heck with you, Los Angeles Times). The July 26, 1941 St. Petersburg Times has a version that uses milk instead of applesauce.
The applesauce versions shows up in the October 14, 1958 edition of The Vancouver Sun with different proportions and a suggestion that it be served with peaches and chocolate sauce. By that time, actual ice boxes–the kind where a large chunk of ice kept food cold–were exceptionally uncommon. But you don’t rename a recipe every time something changes. After all, they’re still hamburgers, not newhavenburgers.
From a box sold in Canby, Oregon.
Ice Box Pudding
1/2 c. applesauce
12 graham crackers
Fold crumbs into applesauce
Pour into pudding dish and chill 2 to 3 hours.