Harry's past makes him extremely protective. He lost his parents at a young age, so he would do anything to prevent Pontya from experiencing such a loss. He would be more cautious and use his own experiences of facing danger to keep Pontya safe.
Well, it could be about Harry using his magic skills to protect the newborn Pontya. Maybe he creates a safe magical environment for it, like a charmed crib. He might also have to fend off any dark forces that are after the newborn for some reason.
Harry Potter would be very cautious while taking care of the newborn Ponyta. He'd first need to understand its nature. As Ponyta is known for its skittishness, he'd have to be gentle. He might ask Hagrid for advice. Hagrid could tell him how to handle Ponyta's hooves properly or how to groom it. Harry would also need to ensure that the Ponyta is not exposed to any dark magic. He could use protective spells around its stable. And when it comes to training the Ponyta, he'd use positive reinforcement, like giving it a treat when it follows a command.
His magic could be used to heal any injuries the Ponyta might have. For instance, if the Ponyta accidentally burns itself with its own flames, Harry could use a healing spell.
Perhaps Severus takes care of Harry in a protective way. When other students bully Harry or he gets into dangerous situations at school, Severus steps in. This could be due to an underlying sense of responsibility he feels, or maybe a growing affection for Harry that he doesn't quite understand himself.
One great fanfic in this vein might be 'The Veela's Care' where Harry discovers Draco is a Veela in a rather unexpected situation. Harry's care for Draco in this story is shown through his protection of Draco from those who might want to take advantage of his Veela nature. It's a really heart - warming read.
Well, maybe Harry discovers an injured snake in the Forbidden Forest. He decides to take it back to the Gryffindor common room and hides it in his trunk. He uses his magic to heal the snake and then starts to feed it small magical creatures. Eventually, the snake becomes his secret pet and helps him out in some tricky situations, like warning him of approaching danger.
Maybe Harry discovers a baby snake in the Forbidden Forest and decides to take it under his wing. He could use his Parseltongue ability to communicate with it and keep it hidden from the other students and teachers.
One possible plot could be that after the death of Dumbledore and with the Order of the Phoenix in disarray, Harry decides to go into hiding alone. He uses his skills in magic, like the Patronus charm for protection and the Invisibility Cloak to avoid detection. He might start to forage for his own food in the Forbidden Forest, using magic to find edible plants and hunt small magical creatures in a humane way. He also spends his time studying advanced magic on his own to become stronger, preparing for the final battle against Voldemort.
Well, Harry might use his magic to make the baby laugh. For example, he could turn the baby's rattle into a little magical creature that dances around. He'd probably also be very protective, like how he was with his friends at Hogwarts.