He'd be more rough - around - the - edges. In Skyrim, it's a harsher world than Hogwarts. He might be less hesitant to use more aggressive magic. For example, instead of just disarming an enemy like in Hogwarts duels, he might use a blasting spell if it means protecting his charge.
As a bride, Harry Potter might have to learn new skills like walking in high - heeled shoes if that's part of the bridal look in the fanfic. He would also have to get used to different social expectations. Instead of being the heroic wizard ready for battle, he could be in a position where he is more of a center of attention in a social sense, which is very different from his usual role. This could make him more nervous or more assertive in demanding respect in this new role.
He would probably be more in tune with death and the afterlife. Since Anubis is associated with death in Egyptian mythology, Harry might have a more solemn and respectful attitude towards it. He could also be more mysterious, as his connection to Anubis would set him apart from other wizards.
Well, the plot could involve Harry using his magic skills in the world of Skyrim. Maybe he's hired to protect a powerful mage in Skyrim from the various threats like dragons or bandits. He'd have to adapt his Hogwarts - learned magic to the different magical rules of Skyrim.
The common folk in Skyrim would probably be a bit scared at first. Harry's strange clothes and the fact that he can do magic so effortlessly would be quite intimidating. But if he helps them out, like getting rid of a bandit problem or curing a disease, they would soon start to accept and even revere him as a powerful hero.
His character would develop a stronger sense of adventure. Skyrim is full of mysteries waiting to be uncovered. Harry would constantly be seeking out new places, new spells, and new knowledge. He'd be less sheltered compared to his upbringing in the Harry Potter series. Also, his relationships with others would be more fluid. In Skyrim, alliances can change quickly depending on the situation, and he'd have to adapt to that, which would make him more adaptable and perhaps a bit more cautious in his dealings with people.
Harry would likely be more wild in a sense. Dragons live by their instincts, and he'd pick up on that. His magical abilities could be more primal. Instead of relying on the spells taught in Hogwarts, he might use magic in a more raw and unrefined way. Also, his sense of loyalty might be more towards the dragons rather than the wizarding community initially.
He would be more refined. Royal upbringing would instill in him a sense of propriety and elegance that he lacks in the original story.
If house - elves raised him, Harry would be extremely humble and have a strong sense of service. He wouldn't have the same pride as he does in the original series. He would also be very good at taking care of details and might be more of a behind - the - scenes helper at Hogwarts rather than the center of attention all the time.
The Dragonborn would be an amazing crossover character. Imagine the Dragonborn showing up at Hogwarts. They could use their Thu'um in the hallowed halls of the school, which would surely cause a stir. The Dragonborn's ability to absorb dragon souls and their combat skills would make them a force to be reckoned with in the wizarding world. They could also learn about the different types of magic in the Harry Potter universe and perhaps use it to enhance their own powers.
He'd probably be more rugged. Skyrim is a harsh land, so he'd be tougher physically. His personality might be less influenced by the refined wizarding society of Hogwarts and more by the rough - and - tumble adventurers in Skyrim.