Lean2Rescue work was shut down on several planned leanto work projects a while back due to the above mentioned snowmobile trail lawsuit in the courts. We couldn't even legally cut small stuff of any size to clear a leanto size footprint, not to mention any larger "danger trees" on site.
No one is allowed to participate whatsoever in L2R (or any other such volunteer work) without agreeing to and signing a formal NY VSA agreement.
https://www.dec.ny.gov/regulations/90822.html
Chainsaws are not generally allowed in wilderness areas, though there are certain times of year when that is possible. If you do use a chainsaw, you must be certified in safe operation by taking a state approved training course (which includes blood-borne pathogens medical training). And you must always wear all approved safety gear during any chainsaw operation, no matter how small the job.
ADK has a trail maintenance course that is given infrequently. Offered just twice last year, but one was cancelled due to Covid. NYSDEC requires this certification for trail workers.