Courtesy of An Aesthete's Lament: "On 3 May 1916, The New York Times ran an article stating that the Mill Neck Club's club house was the property of Irving Brokaw. However, the building was then being physically moved from Oyster Bay to Glen Cove. An earlier article about Brokaw's purchase of the building and its land (27 September 1914) called it the Mill Neck Gun Club, "one of the oldest organizations at Oyster Bay"—so it was a shooting club rather than a skating organization, though arguably that could have happened there too. The property was stated as being 105 acres in size, and that Arthur D Weekes was the president of the club."
You can still make out what looks like the driveway running along the pond when you look at it from google earth. Above is the view looking into the property, below is the view looking out towards Oyster Bay Road.
Update: Arthur Delano Weeks, the president of the Mill Neck Gun Club, lived just east of Lower Francis Pond at the intersection of Beaver Brook and Oyster Bay Glen Cove Roads. He was an attorney and mayor of the Village of Oyster Bay.