This blog mentions a 1953 78-rpm children's record: "Ken Jay and Cricket Chorus doing FROSTY THE SNOWMAN b/w THE LITTLE CHRISTMAS STOCKING WITH THE HOLE IN THE TOE."

Record Collectors Guild describes a 45-rpm record on the Cricket label, CX8, and says the singers are The Cricketones.

eBay.ca lists an LP called "Christmas Is for Children" that contains the song.

Some web sites give the title slightly differently, as "THE LITTLE CHRISTMAS STOCKING WITH A HOLE IN THE TOE" or "...IN ITS TOE". (Such small differences can be crucial when using a search engine.)