This is my first time posting, so hopefully I won't leave out any details.
I read this YA book about ~15 years ago. It was about a princess/daughter of a king who was sent to the desert/uncivilized nation to be married to this prince. When they first met, he thought that she was a "dancer" because she was so dressed up, and that she was there to entertain the guests. However, they ended up going on a journey together (forget the reason why), but she found that his culture was not so barbaric as she had heard. There was magic but I am forgetting what role it played.
There is one scene that I still remember - he mocked her for using the same toothbrush everyday (because that was gross to him). He used a fresh new twig-toothbrush everyday and was more minty-fresh/cleaner than she was.
It was a paperback book. I think the cover was yellow with a sun. Honestly, it might not even have been YA. I'm not even sure if she was arranged to be married to the prince or if she was being forced to visit (I'm fairly sure there was some romance at some point).