Tough one. Likely going to be best to leave as a recording that faithfully represents the blowing trees as part of the auditory experience, but "intelligent" noise reduction is getting smarter all the time, so worth a try with a noise-reduction routines that are based on inputting a sample of the noise - a snippet of the recording that contains only the blowing tree noise and as little of everything else as much as possible (music, audience, whatever else). I suspect that may work better than a noise-reduction routine specific to wind-noise because the profile and spectrum of the tree rustling noise is likely to be quite different from that of wind blowing directly on the microphones. Still, worth giving that angle a try too.
Best way to minimize this prior to recording is getting a lot closer to the source, so that the source is much louder in comparison to the trees.
Sounds like a sweet venue with musically astute owners.
Not the same scenario, but made me remember a recording I made a few years ago made in a really nice outdoor open-air log shelter up in the Western NC mountains that is fantastic except for the sound of a creek rushing in a gully behind the stage that lays atop the entire recording like a heavy blanket. Rather than sounding charismatic and bubbly like a babbling brook, it sounds like the charmless loud white noise hiss experienced on an airline flight. The irony is that in the performance space no one could really tell the creek was even there, visually hidden by shrubbery. The sound of it was effectively inaudible at head height, but I hoisted the mics up high in front of a big log column to visually minimize my intrusion and minimize pickup of audience chatter, and unfortunately from up there the stream was pretty much in a direct line behind the performer making it very audible. I plan to revisit this one someday to try and address the noise, as otherwise its a great performance.