Frozen wood is harder to chop...
Contrary to what some might say, wood does freeze; milled lumber, timbers, seasoned logs, green logs, even standing live trees. But it doesn't freeze at 32° F, rather depending on the species and the moisture content, the point at which wood freezes is considerably lower and it needs to remain there for a considerable period of time. Standing live hardwoods will typically freeze if temps remain below -15 for at least a couple weeks --- For softwoods, -20 for about 2.5 weeks. This is because the "free water" in trees (or wood) is more like a diluted anti-freeze due to dissolved sugars and minerals.
Most trees that are native to the more northern areas of the USA do not typically die when frozen solid because the "bound water" which is actually part of the cell structure of the "living cells" has this natural antifreeze characteristic, and that, along with physiological changes that happen to moisture location (on a cellular level), allow these cells to stay slightly unfrozen and alive... Even when the majority of the trees mass (dead cells) are frozen and the free water between the cells and within the vascular system has turned to ice.
In freshly felled, or "green wood" the bulk of the wood's moisture content (expressed as a percentage) is "free water". This is why when green wood freezes it gets so much harder. It is basically ice reinforced with wood fibers, and ice is harder than all but the very hardest tropical hardwoods. It should also be noted that a felled tree will freeze considerably easier that a standing live tree.
Because of this many non-heated saw mills will not process frozen logs, and many of those that do will debark and thoroughly remove any exterior ice before sawing. They may also decrease the tooth angle and change the "set" on their saws teeth, or they change over to special "winter teeth".
The same is true for chain saws used on frozen trees; change the tooth angle, adjust the raker height, or change to a carbide tipped winter chain. Even before the time of chain saws, loggers that had to work with frozen trees or logs, sharpened their crosscut saws differently for extremely cold weather, or had designated winter saws for use on frozen trees.
The amount that wood hardens when frozen depends on the species and the moisture content. Certain hardwoods, like red oak, get noticeably harder. Others like most of the maples can get significantly harder. Many of the softwoods can get dramatically harder because of their higher moisture content when green. More frozen moisture means harder wood. White Fir is probably the worst because even in the winter its moisture content percentage can average well over 100% when freshly felled.
The harder the wood, the harder it is on the tools used to work it. Frozen wood is especially bad because not only is it harder... But it also becomes brittle. Rather than the fibers cutting with typically longer shavings, they instead break or shatter into much finer dust and finer dust is harder for the blade to clear from the cut, not to mention that it can also build up along the sides of the blade's body if the amount of set isn't reduced accordingly. Because of this, and also because frozen saw dust is very abrasive, blades dull much quicker. It's like the differences of how a sharp chisel cuts wood as opposed to how a file "cuts" wood.
Edged blades (axes, hatchets, brush axes, etc.) are more difficult to use and "cut slower", the harder the wood is. Again, some of this can be mitigated by the way the blade is sharpened, but sharpening will need to be done more frequently. The typical way that a hardware store axe is sharpened can result in an axe literally bouncing right off of a smallish frozen fir tree… almost like it was a rubber mallet.
And being a master wood worker, I can tell you to never try to mill or machine frozen lumber… Teeth and knives dull very quickly, saw bodies scorch and lose temper. Feed rollers and feed wheels don't grip. Not to mention that frozen boards can release internal stresses much more violently than non-frozen boards which can result in severe "kick-backs".
On the other hand, most species of " bucked up" fire wood are considerably easier to split when thoroughly frozen. This is because the frozen connective fibers have less adhesion to each other and the icy wood is far less compressible… making splitting wedges and splitting axes far more efficient. In fact some people do most of their "green" fire wood splitting when their wood is solidly frozen.