How should I remove a wooden fence from a tree trunk?
I would have to agree with Ed, with the added suggestion that a SawzAll might be used on the fencing if nails are an issue, or if you don't have a chain saw. The smaller size might also work better if the clearances between objects that are being cut are such that a chain saw might be unwieldy.

But, yeah, chain saw rules otherwise.

Be safe,
Bill