What were Aram's earliest memories, and what was he longing for in "The Summer of the Beautiful White Horse"?

At the beginning of the story, Aram says that his earliest memories had been "memories of horses and (his) first longings had been longings to ride." However, because his family has always been very poor, and unable to afford their own horse, Aram's longings to ride have been generally frustrated. This is why he is so delighted, although also amazed, when his cousin, Mourad, shows up at his window one night astride "a beautiful white horse."
When Aram finally gets to ride the horse alone, he is thrown of,f and the horse runs away. He can't manage a horse like his cousin can. One reason why Aram and Mourad decide to keep the horse for longer rather than return it to its lawful owner is so that Aram can have time to learn to ride the horse on his own. Unfortunately for Aram, the boys are discovered with the stolen horse by the horse's owner before he can learn how to ride it on his own. His longings to ride alone are thus frustrated.