I think it's the same with these wooden machines, most I see are in the US and not subject to UK atmospheric changes.
Here in Michigan, we're surrounded by water, so we can get very high humidity in the summer, and very dry and cold winters. I have a wood machine, and it's 11 years old. It's no different than the day I built it. As Sven said, you just need to seal it properly. The problem with 99% of wood machines, is that they rarely get sealed and finished properly, and are usually poorly engineered to start with.

I'm currently working on a 4x8 dual spindle wooden machine. It's very complex, with lot's of laminated materials, bonded in phenolic for rail mounting surfaces (cnc machined straight and flat), and lots of aluminum for mounting surfaces (motors and drivetrain components) and brackets. And lots of epoxy.
It's a lot more work then building with steel, but I find it easier and far more enjoyable than working with steel. But it definitely takes a lot longer, and requires a lot more thought when designing.
You can easily weld two pieces of steel together at a 90° angle, and get a very strong joint. Try to do the same with wood, and it's much more difficult, and will almost always be a weaker joint.