Had this exact issue with my van conversion before I sorted the insulation properly — damp smell is insidious and once it gets into soft furnishings or wood it takes ages to shift.
For a log cabin office I'd say a dehumidifier is almost certainly worth it, yeah. The timber breathes and after heavy rain it'll absorb moisture, especially if the ventilation isn't great. A decent unit will pay for itself in protecting the structure alone, never mind making it actually pleasant to work in.
A few things worth considering:
- Size matters — match the unit to your cabin's volume, don't just grab the cheapest
- Running costs — these aren't trivial if you're on mains, worth factoring in
- Off-grid angle — if you've got any solar feeding the cabin, a compressor-type dehumidifier on a timer during peak generation hours is a tidy solution
- Address the root cause too — ventilation, vapour barriers, any gaps around the base?
I've been running a smallish compressor unit on my boat during winter and it's transformed things. Meaco seem well regarded for UK conditions — their units handle lower temperatures better than a lot of the cheap imports.
What's your cabin built on — concrete base or timber bearers? And is it insulated at all? That'll change the advice quite a bit.