courtesy of @perzysprumia :
because of hope's stark blood, she too is a warg. this wasn't discovered as a separate thing because of the magic she's been capable of since she was a small child.
it's not until she meets and bonds with the dragon viserion and able to warg into him does it become clear that hope is a skinchanger.
hope bonds deeply with the dragon, seemingly able to speak to him without words (this could be due to magic or because of her bond as a warg, it's hard to tell)
acting on instinct, hope climbs atop the dragon's back when she stumbles upon him and rhaegal in the catacombs of the city. she tells no one of this and continues to sneak down to the dragons when she is able.
they continue to bond as dragon and dragonrider while daenerys is away. secretly she hopes that the dragon queen will never come back and that hope can take this dragon for herself.
when daenerys returns to meereen during the second siege with drogon, hope frees rhaegar and viserion from the catacombs to turn the tide of the battle.
hope is seen atop the back of the white dragon for the first time.
while sailing with the dragon queen back to westeros, hope takes any opportunity to ride her dragon as she can, though she does not travel too far at her father and uncle's request for safety.
during the wight hunt beyond the wall, hope rides on viserion's back, ignoring the protests of tyrion, klaus, and daenerys.
when the white dragon is struck by the ice spear, hope remains on his back. during the uncontrolled fall. hope is protected by viserion and survives the fall as the dragon falls helplessly into the frozen lake.
hope refuses to leave her dragon, having resulting in klaus pulling his daughter away from the broken ice and forcing her onto drogon's back.
hope is devastated at the loss and becomes inconsolable about the dragon's death, stating that it was like losing most of herself.
hope is not seen again by most, seemingly locking herself in her quarters at dragonstone and refusing to come out or let anyone in. the only two people who are able to speak with her directly are daenerys and later, jon snow when he returns.
hope is not seen by anyone else until it is time to march north to winterfell and fight the oncoming army of the dead.
hope remains an impassive presence at winterfell, secluding herself from most matters and only showing face during meals. most times the young girl is found in the godswoods nearby.
during the second battle with the night king, when viserion is shown to be under his control, hope makes a dangerous attempt to save her dragon.
using her warg abilities and the connection she once had with the dragon, hope is able to break the night king's control of the now ice dragon and saves viserion from a second death just before the fall of the night king (this is in part to her warg abilities but also coupled with her magic & targaryen blood is hope able to do this)
when asked how she managed this, hope does not know and says as much. she does not wish to find out and never intends to do such work again
viserion remains an ice dragon though his wounds are less disfiguring and he does not appear to be undead at first glance. his appearance changed after the night king's resurrection of the dragon, changing the gold points of the dragon to an icy blue and white coloring.