Yes, I remember the St Francis Riding Academy (SFRA) very clearly.
In 1940-46, I lived at 672 7th Ave, a half a block from the SFRA. We played in/around the big red brick building all of the time. I attended Star of the Sea Grammar School.
I have very clear memories of the equestrian shows where us kids would sit upstairs in the ring above the arena. In 43-44?, a sad occasion occurred when a horse+rider came out of the stable on 7th Ave and slipped on the pavement. The horse broke a leg and was in serious condition. A few minutes later a man with pistol came out of the big brick building and shot the horse. A sad day, unforgettable day for us kids.