When I finally connected my aerial to Hudson Valley CC I contacted the Westchester Historical Society to see if they had any information on the club. They sent me this excerpt from a history of golf in Westchester written by Wm Quirin of the MGA.
"The St. Andrews story has a footnote. During the 1890s the unwritten policy at St. Andrews regarding lady golfers was simple: To the ladies, God bless them, always welcome but never invited. So in 1895 a group of St. Andrews women, led by Mrs. John Reid, Janet Waring and Frances Gilman, organized the Saegkill Country Club. They leased land and a cottage from John Waring off North Broadway, about one mile north of Yonkers and the Westchester County line. By April 1896 the club numbered approximately 100 members, the majority women (although the first president was J. Harvey Bell), and a six-hole golf course was built for them by Henry Tallmadge and John Upham. In 1900 the club bought some property off Odell Avenue in Greystone, and moved, building a new clubhouse and golf course there.
The Saegkill experiment--a majority of the membership and executive committee being women--ended in 1915 when the men took over. They changed the club's name to the Hudson River Country Club, and engaged Donald Ross to modernize the golf facilities.
In its later years, Hudson River was owned by Dr. and Mrs. [first name unknown] Whiteman, she being a tobacco heiress. They controlled the club's membership, admitting only people they personally liked. Annual fees were relatively inexpensive, but the head count dwindled over the years. When the Whitemans died (both in their nineties), the club had to be sold to pay the estate taxes. The remaining members could not match a $3,000,000 offer made by Boyce Thompson, a horticultural research center. The club closed its doors after the 1968 season, and today the property is part of the Lower Westchester Industrial Complex."
I visited the site several years ago and took photos of what remained of the Boyce Thompson center (it may be gone now), the site of the clubhouse and the still-standing gates, and a few other photos of the surroundings. I can't locate them but if I do, I'll post some.