I have some knowledge about one of the courses on this list. The Onteora Club started playing golf in the year indicated (1887). 5 holes were laid out in one part of the club. The current 9 hole course was constructed in 1905 in a different location than the original layout (the old layout is now an arboretum and cemetary). The 9 hole course was originally designed as 18 holes, but only 9 holes were built. Too bad because in the mid-20s, a large lake was built in what would have become the 2nd 9 holes. Interestingly, the current 9 hole course is almost exactly the same as when built nearly 100 years ago At 3100 yards, par 35, the golf isn't bad and the scenery is the best in the US. During the 1980s, the PGA pro constructed a number of alternate tees so each hole is different the 2nd time around; and on the second 9, the par is different for 2 of the holes, playing into the same green. The architect is not known.
As one poster suggested, this particular club is/was a social club, and was founded for reasons other than golf. More appropriately, Onteora is a Field Club. However, the date indicated for golf is accurate and well documented in the Club History.