I don't remember when the rides closed- but, around 1944 or so, when I was 8, the ponies were being kept at the New Parkway stables. My father thought it would be fun for me to have a ride and so lifted me up and the ride began in the pen. Somehow, the pony got spooked and fled out of the pen and made a fast beeline for the stables.
He not only reached the stables in record time but actually went up the ramp to the second floor stalls where he considered 'home'.
My father and at least one of the pony handlers were in frantic pursuit as the pony and I thundered through the park to the stables. THey were horrified and I was having the time of my life. By the time they reached us, I was breathless and hooked on riding. Bless my father, as scared as he was he recognized that somehow he had a natural rider on his hands and lessons began shortly afterwards. I still love the memory of that pony!
I'm 58 and I recall getting taken to a pony ride at Lincoln Park which would place it in the 60's. Now I know it wasn't in the zoo if that's what you are referring to. But I also remember that the rides where near the old viking ship that was left over from the Columbian Exposition. The rides were just around a circle and I'm thinking maybe there was a person walking along but I'm not sure. But I definitely do remember doing this with my cousins and godmother.