Last year my friend and I were riding in the Game Lands in Bradford County, PA, not far from the NY border. It was broad daylight and a mountain lion crossed the road about 15 yards ahead of us and froze. We watched it for a few minutes then it vanished into the underbrush. We turned around and headed back to the barn. The big cats aren't supposed to be in our area but we told our story about seeing one, and everyone at our barn had either seen one or knew someone who had.
I would be careful riding in Central NY and Northern PA - mountain lions are out there.