Whenever I would hear someone do this song (which would have been back in the 1970s, my Cornell Folk Song Club days), they would do the version of the chorus that went "the winter winds begin to blow, the ground is covered up with snow", as opposed to the New Lost City Ramblers' version, which omits "with snow". In order to make the chorus scan, the next line would be shortened, something like

... the winter winds begin to blow, the ground is covered up with snow.
You think on the way ...

I believe that folks tended to do the New Lost City version, but with inclusion of with snow.

Or maybe my memory is bad!

Don