I have played Mohawk a bunch over the years going back to High School matches in the mid to late 70's. To me it is a perfect example of a course that you could play every day for the rest of your life and die a happy man. It has a great mix of holes; long, short, difficult, easy, etc. It is also has interesting green complexes and is simple to walk.
Tom Watson did an exhibition there several years ago and he loved the course.
Although it is private it is not impossible to gain access. The Head Professional, Jeremy Kerr, is a terrific and friendly guy. I would imagine that fall would be a good time to try and get on there as play seems to really drop up here after Labor Day.
Truly one of my favorite courses in all of upstate New York.