I’m hoping someone here can help me pin down the origin of a children’s song

Here are the lyrics as I remember them:

In our backyard we made a friend,
He's not like you or me.
His eyes and nose and smiling face
Are all of coal you see.

We made him by the window,
So every morning bright,
He could look right in and smile at us,
He's such a cheery sight.

Snowman, snowman on our great white wall,
Snowman, snowman hear us gayly call.
How we wish that you could always stay,
But we know that you will melt away.

And just that very morning,
We missed his cheery smile,
When we came out to look for him,
We found a little pile.

The snow lay all around him,
Where he had stood you know,
The ground was wet with snowman tears,
How he had hate to go.

Snowman, snowman on our great white wall,
Snowman, snowman hear us gayly call.
How we wish that you could always stay,
But we know that you will melt away.