Not sure yet. I've got equal parts A:tLA and Game of Thrones in the back of my head, although I'm fairly certain neither one of the main ladies is from a horse-barbarian culture. Although I am wondering if maaaybe Prince Prima and Prince Secundus are from semi-nomadic types- settled and successful enough to have time/leisure/money to get fancy with their clothes/tents/learning/magical practices/treasures, but with a life that requires being active and practical, defending valuable herds and people. Sophisticated Mongolian horde/ancient Celt feel- a prince's major duty might involve defending the royal herds (or a supplicant noble's) from other raiders.

Not sure about Princess Frost-hair's kingdom. I feel like at least this palace the tournament's being hosted at is on the edge of the desert, but she's totally yoinked from both Daenerys Targaryen as well as Yue, so it's possible her heritage comes from a couple different places that ended up conquering the lands her kingdom currently dominates, with some magic thrown in.

Since it's a tournament there's probably representatives of other kingdoms floating around as well that I'll need to think about.