Amazing to find this thread. I was searching to find out the origins of this little ditty my grandfather, Calvin Bryce Hoover (1897-1974), used to sing. Even though these lyrics are a little different, to me they're the right ones, because they were the way he always sang it.

In de vinter-time, in the valley green
When the wind blows on the window panes
And the washer-women in the waterworks
Ride velocipedes in the vestibules.

And that's all of it that I ever remember hearing. Quite a mystery it has always been to me, and this thread hasn't gotten to the bottom of it either!

I probably heard it from him sometime in the early 1960s.

Even if someone made up the 'washerwomen in the waterworks' to avoid women being in vaudeville, to me the washerwomen phrase has a wonderful sing-song rhythm that also evokes a Scandinavian accent.