Yes, my class, 1945, had "Equestrian Classes" as did the Class of 1946, but I am not sure about '47-48.
When my class graduated in June 1945, Thayer Hall had not been rebuilt from a riding hall and the space across from the Thayer Hotel was known as "The Cavalry Plain" and faced stables where there were horses.
In a search on buildings at West Point I found this phrase about Thayer Hall; "used for equestrian instruction until riding was removed from the curriculum during WWII..."
Actually as I remember the "stern eye" was that of the Cav officers who conducted the training, while the 10th Cav troopers took care of the horses and had them saddled and ready for the cadets to mount. It seems that my dislike of horse riding has removed most of my memories of the hours in the riding hall and at the Cav Plain. The Cadet Mess waiters were troops from the 10th Cav impressed into that work when most, if not all, of the civilians found much better paying jobs in the ship building and other war businesses in NJ and other areas.