So, I finally figured out a cutie mark and name (and made a very slight adjustment to haircolour).

Meet Princess North Star. She patrols the Crystal Empire and its frozen surroundings to make sure no one gets lost and guides travelers safely from one place to the other, bracing any dangers along the way. She is very friendly and likes to surround herself with the common people, always being curious about their lives and stories. Shes a bit fickle when it comes to her princess title and the fuss surrounding it, so shell often disguise herself and refer to herself as just Star. While not outright rejecting of her parents, she tends to get a bitflighty when faced with the palace surroundings. She only got her cutie mark very late after sneaking out of the palace to help in the search (and consequent return) of a lost foal. A princess of the people.