Here's the entry from the Traditional Ballad index, which states the song may have traditional roots. Anybody have access to the cited issue of Wisconsin Folklore?

Frozen Logger, The

DESCRIPTION: The singer meets a waitress. She recognizes him as a logger, and tells him the sad tale of her amazing logger lover. One night he forgot his Mackinaw, and at last, "at a thousand degrees below zero, it froze my logger love."
AUTHOR: James Stevens (1892-1971)
EARLIEST DATE: 1951
KEYWORDS: love logger death talltale
FOUND IN:
REFERENCES (4 citations):
Lomax-FSNA 61, "The Frozen Logger" (1 text, 1 tune)
Silber-FSWB, p. 30, "The Frozen Logger" (1 text)
DT, FROZLOGR*
ADDITIONAL: Walker D. Wyman, _Wisconsin Folklore_, University of Wisconsin Extension (?), 1979, pp. 35-36, has a version, quite different from the Weavers text, which he apparently thinks is traditional folklore
Roud #5470
NOTES: There is a good deal of uncertainty about the author of this. Not that there is any question that the author's name was pronounced "James Stevens"; all seem to agree on this. But different sources have spelled it "Stevens" or "Stephens."
Research by Abby Sale and others supports the theory that the author was the James Stevens whose dates are cited above; he also wrote the classic book Paul Bunyan in 1925. The "Stephens" spelling may possibly be by confusion with the Irish author James Stephens.
According to Sing Out!, Volume 37, #3 (1993), p. 72, Stevens based this on an actual lumberjack tall tale. But, of course, Stevens also claimed his Paul Bunyan stories come from that source -- and many of them clearly came out of his head.
It may be questioned whether this is a folk song. I would not so count it, despite its inclusion in Lomax. Nonetheless, the versions have been folk processed to a certain extent -- notably in the first verse, where the original version read "A six foot seven waitress." Somebody (the Weavers?) converted this to the unremarkable "A forty year old waitress," and of course this has been common since, even though the line is banal and does nothing to enhance the tall tale aspects of the song.
There is some interesting science (or, perhaps, lack of science) here. There is, of course, no such temperature as a thousand degrees below zero, in either the Farenheit or Celsius scales; Absolute zero is at -459.7 degrees Farenheit -- and anything not made of helium (which is everything more complex than a single atom) will have frozen rock-solid far warmer than that.
But it is in fact not unlikely that the logger was hard to freeze. Assume the logger's girl was, in fact, 79 inches tall. This would make her at least 15 inches taller than the average woman of Stevens's time. That's 23% taller. Presumably her lover is also about 23% taller than average. (For the time, that makes him an inch or two above seven feet.).
And that brings in what is called the "square-cube law" or "the law of squares and cubes": That the surface area of an shape increases as the square of its linear dimension, but the volume increases as the cube of its linear dimension. In simpler terms, as something gets bigger, its surface area gets smaller relative to its volume. By a lot.
Which is significant, because the heat generated by a body is roughly proportional to its volume, but heat loss is roughly proportional to surface area. The fact that the logger was very big did make him significantly less vulnerable to cold (though more vulnerable to heat). So while this is a tall tale, it's a little less tall than it might have been.- RBW
File: LoF061

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Here are the lyrics from The Folk Songs of North America (Alan Lomax, 1960), #61, page 120-121.

THE FROZEN LOGGER
(James Stevens)

As I sat down one evening Within a small cafe,
A forty-year-old waitress To me these words did say:

'I see you are a logger, And not a common bum,
For no one but a logger Stirs his coffee with his thumb.

'My lover was a logger, There's none like him today;
If you poured whisky on it, He'd eat a bale of hay.

'He never shaved the whiskers From off his horny hide,
But he drove them in with a hammer And bit 'em off inside.

'My logger came to see me On one freezing day,
He held me in a fond embrace That broke three vertebrae.

'He kissed me when we parted, So hard he broke my jaw;
I could not speak to tell him He'd forgot his mackinaw.

'I saw my logger lover Sauntering through the snow,
A-going gaily homeward At forty-eight below.

'The weather tried to freeze him, It tried its level best,
At one hundred degrees below zero He buttoned up his vest.

'It froze clean through to China, It froze to the stars above,
At one thousand degrees below zero It froze my logger love.

'They tried in vain to thaw him, And if you'll believe me, sir.
They made him into axe-blades To chop the Douglas fir.

'And so I lost my lover, And to this cafe I come,
And here I wait till someone Stirs his coffee with his thumb.'