Link uses the potion on Epona.

That night, Link couldn't help his eyes drifting towards the potion. The old woman had said it would allow him to grow closer to an animal, and there was no animal he wanted to get closer too than Epona. After all, the mare was his faithful steed, he'd known her since she was a foal and he a boy. But for that same reason, he was scared to just use some random potion given to him by a mysterious woman on Epona. What if it hurt her? What if the woman was allied with Ganondorf, and this was merely a ploy from the evil man?

But as he began getting sleepier, and he was getting ready to camp out in Hyrule Field for the night, the lack of sleep was starting to affect his mind. Without remembering the caution he'd thought of beforehand, Link tiredly spread some of the potion on his hands and pat Epona's fur before going to bed. He told the horse he loved her, and wanted to get closer to her. As the hero fell asleep, he had no idea how much his wish would come true.

Waking up the next morning was odd. Right away, Link was confused why he seemed to be standing up, rather than lying on the ground, on a bedroll. Looking down, he could see the bedroll was still there, but that was when he noticed something else odd: was it always so far down to the ground? Clearly, it seemed like he'd become taller. Confused, Link looked around a little more, and immediately noticed the problem: he was no longer a normal Hylian.

From the waist down, his body was that of Epona's, a mare's, a horse's. From the hooves on his feet to the furry butt on his end, Link had the entire lower body of an animal. But the changes didn't stop there. Where the horse part transitioned to something more human, Link's skin was more tanned than before, and from the corner of his eye he could see his hair had gone from blond to auburn. But more than that, was that there was nothing masculine about him any more. His arms and torso looked and felt utterly feminine, and under his still-green tunic, he could see a fairly large pair of breasts hid themselves inside. That potion had made him closer to Epona, alright, but only by fusing the two of them together.