What is the origin of the term "button nose?"

As the title says, I would like to know the origin of “button nose”–the year, the part of the world, first use in publication, anything would be helpful. I know it was used in the song Frosty the Snowman in the late 1960s, America, but that’s basically it. Can anyone help me?

Well, if it helps, “Frosty the Snowman” was written by Jack Rollins and Steve Nelson, and first sung by Gene Autry in 1950. They also wrote the song “Peter Cottontail”.