I have read a few articles and all say it isnt impossible but may not be an easy task? Would it be more likely approved if livestock kept in the woodland and the owner to be on site for welfare?
What type of structure are you hoping to build? I think you would have to be at the extremes of ecological design - turf roof, passivhaus, subtle access. It would also of course depend on what animals you intend to keep in the woodland and which particular woodland you have in mind. I think the rules on damage to rural trees have changed since I knew about TPOs so you would have to use very non-intrusive building methods.
I have read about lovely woodland houses getting the go-ahead but my impression has been that they are all architect designed, high status constructions winning awards, and the little straw houses or lath and cob buildings don't seem to be mentioned. There are bound to be discussion forums more specialised than TAS which could let you in on the secrets.
Actually I think that unless you were intending to live in a clearing perhaps then keeping animals might be a drawback because of the risk of damage to the trees.