Not the right song, apparently, but a similar theme, from the sheet music at Indiana University (Click for the PDF file.):

WHEN THE MOON SHINES DOWN IN OLD ALASKA (THEN I'LL "ASK'A" TO BE MINE)
Words, Jack Frost. Music, E. Clinton Keithley.
Chicago: Frank K. Root & Co., 1916

1. Northern lights are softly gleaming
O'er the silent sea.
Northern lights so brightly beaming,
Seem to beckon me.
They remind me
I left behind me
A girl with heart so true.
Northern lights will always find me
Dreaming all night through.

CHORUS: When the moon shines down in old Alaska,
Then I'll ask her to be mine.
There are two blue eyes in old Alaska
Bright as Northern lights that shine.
She's a golden nugget
Up in a northern clime,
And I'll hold and hug it
While both our hearts entwine.
When the moon shines down in old Alaska,
Then I'll ask her to be mine.

2. Moonlight now is softly glowing
On Alaskan shore.
Moonlight seems to know I'm going
Back to her once more.
For I love her;
The stars above her
Help to guide my lonesome way.
Moonlight knows I'm dreaming of her
And that happy day.