Funnily enough, husband and I have been having the hot-tub-in-holiday-let argument for a few months now.
As I understand it, the idea behind a hot tub is that it stays on all the time and doesn't need heating up to get into (my brother-in-law worked out his costs him 65p a day to keep going), so I'm not quite sure how that would work with wood-burning.
If it doesn't have the standard chemicals in, you might also be laying yourself open to a claim if someone came down with something that could have possibly been water-borne after using it.