Hi Nomada
This wet woodland wouldn't be in the Glaslyn estuary by any chance?
The first thing I'd offer to think about is that although it's rained plenty in the last fortnight, here in North Wales we've had the driest start to the year since 1929 - so however wet this wet woodland seems probably it's typically much wetter!
Wet woodlands need drainage ditches that are maintained - trees other than alder are not able to maintain root systems deeper than the average water table in winter. If it's a young wood everything may seem fine- but as the trees get bigger they offer more of a sail to the wind, then if the water table starts to get too high (i.e. ditches not maintained) then the trees will become unstable and may blow down suprisingly easily.
That said Natural wet woodland is a wonderful habitat - if you're happy to have a tangle of blown down but regrowing trees of all shapes and growth forms of suitable species (willows, poplar, alder and a bit of ash on the drier bits) - and not insist on trying to force it into looking like the usual 'ideal' of woodland - then it can be one of the most rewarding forms of woodland from a conservation point of view, with the least effort of management. If you leave any prejudices of how woodland 'should' look, and don't to try force it into the 'standard' model, with loads of unsustainable management, but just go with the flow, then I'll bet you'll really enjoy your time with the wood.
I'd suggest going and visiting other wet woodland (woodland trust, knock on farmers doors if they have any welsh woodland with gwern in the name on the os map)just to really get a feel for the unique atmosphere of wet woodlands to see if it's really your thing.
It would be easy enough to make a nice dry area for camping in even the wetest woods - I would expect you'd pay approx. £200 in North Wales for a contractor to dig you a nice pond and to shape the dug out spoil into a raised level mound suitable for camping - although of course you wouldn't mention that was the intention!