Timber framing uses dry wood as well, slightly different techniques but in the softwoods and some of the hardwoods its is not all that harder to work dry than green and in some ways easier. It depends on the tradition and location as to the exact process and technique, some preferred dry timbers, some green, some something between.

In US farm country it was common to fell the trees in late fall/early winter after the harvest was all taken care of and then leave the trees where they dropped until the ground froze. After the ground froze you haul them to the build site, much easier to drag logs on hard frozen ground than on soft wet ground. Then you would forget about them until after the spring planting is taken care of and build in the summer. Those big timbers would be far from dry but they will have lost a fair amount of weight and will be more stable which makes everything easier.

Wood expands and contracts with moisture content. More moisture makes the fibers "fatten up".

The interesting thing is that this is anisotropic: the expansion/contraction occurs across the grain, NOT along the grain. The rate of expansion also depends on the local characteristics of the grain itself (hence the effects of warping due to uneven expansion) ... Also there's a big difference between the direction "across the growth rings" (i.e. radially when it was still a tree) and tangentially to the growth rings. And these surfaces are curved, of course. But one thing we can always say is: the wood doesn't significantly change size along the grain.

Design and construction methods can make wooden artifacts more or less susceptible to cracking and distortion from this. For example dovetail joints can be pretty good as all the wood expands/contacts together the same way. Especially if the pieces are joined together from the same piece of wood. Stuff like that. Or at the other extreme, metal fixings like nails don't move with moisture at all, which can cause problems with relative movement and stress can accumulate.

Edit: and the repeated cycling of moisture content induced stress can eventually lead to cracking, in a similar way to metal fatigue. Old wood just cracks sometimes, this is probably why.