Someone, across at the now-closed 1000Huts forum, asked if they can claim VAT.
A hut is not a residence: it does not qualify for VAT refund. A holiday home only qualifies if it is built / planning-approved as a residence / dwelling.
You could, possibly, register a business, operate the hut as part of the business (forestry uses, holiday rental: it is not excluded and is not STL), and claim it back but is it worth the hassle?