The text containing the earliest occurrence that I have found of the books won’t freeze explains the meaning and purported origin of this U.S. phrase; this text is Western Words: A Dictionary of the Range, Cow Camp and Trail (Norman, Oklahoma: University of Oklahoma Press, November 1944), by Ramon F. Adams (1889-1976), U.S. cowboy, musician, folklorist and author of books on western Americana:

book count
Selling cattle by the books, commonly resorted to in the early days, sometimes much to the profit of the seller.
books won’t freeze
A common byword in the northwest cattle country during the boom days when eastern and foreign capital were so eager to buy cattle interests. The origin of this saying is credited to a saloon keeper by the name of Luke Murrin. His saloon was a meeting place for influential Wyoming cattlemen, and one year during a severe blizzard, when his herd-owner customers were wearing long faces, he said, “Cheer up boys, whatever happens, the books won’t freeze.” In this carefree sentence he summed up the essence of the prevailing custom of buying by book count, and created a saying which has survived through the years.

The second-earliest occurrence that I have found of the books won’t freeze is from Let’s Go Western!, by Segundo Bill, introducing an advertisement for The Western Shop, which sold “typically Western” leathercraft and gifts—advertisement published in the Long Beach Independent (Long Beach, California) of Sunday 6^th January 1946:

“BOOKS WON’T FREEZE” . . .
In the boom days when greenhorn capital was racing to buy Western cattle ranches, many a ranch was sold on the book-count . . . if a hard winter killed off part of the herd the wise ones used to say . . . “Shucks! The books won’t freeze” . . . the tenderfoot who bought in the winter often had to hunt for his stock in the spring.

Advertisement for The Western Shop—Long Beach Independent (Long Beach, California)—6^th January 1946:

The phrase then occurs in The Wyoming Bubble, by the U.S. author of westerns Allan Vaughan Elston (1887-1976), published in the Daily News (New York City, N.Y.) of Sunday 12^th June 1955:

“Don’t put too much trust in a book tally.”
The man from Boston laughed. “I’ve been warned about that. Book tallies are a standing joke at the Cheyenne Club.”
“The joke started,” Russ explained, “in Luke Murrin’s saloon one cold winter day. Bunch of cattlemen were in there during a blizzard, worryin’ about how many steers’d die in the drifts. Luke drooped an eyelid their way and said, ‘Cheer up, boys; the books won’t freeze’. Meanin’ that some brand owners just let the fall book tally stand all winter and sell out next spring on that basis, no matter how many head froze or got stolen over winter.”