Does ice get colder than 32F/0C? If it does, is it harder then?
It might help us understand what chopping in cold temperatures does to the axe.
From a life time 'somewhat-northerner' (Ottawa ain't all that cold compared to Winnipeg, Kapuskasing, Timmins, Saguenay, Edmonton etc) the answer very much is 'yes'. Complete your next cocktail Martini refill with -40 F (preferably even colder) ice cubes and see what happens. Guarantee you'll be impressed! Professional hockey players and figure skaters of the modern 'man-made ice surfaces' era are entirely unprepared/overwhelmed by the properties of bona-fide cold-hardened ice.
Folks in Iqaluit and Yellowknife do not buy vehicles with alloy wheels; at -40 to -60 these rims shatter like glass first time they bump a rock or kiss a curb, even steel wheels are fragile in that environment.
Walters Axe of Hull Quebec catered to professional loggers throughout Canada from the late 1880s until the early 1970s and their motto was "not too soft and free from flaws". I'm guessing a modest slogan such as this wouldn't have meant much to lumbermen in Texas, Arizona or the tropics.