If you ask me, I think Frosta, like most of the other Princesses, got completely screwed over. Frosta didn't have much overall screen time (at least in my opinion) and we know Jack-Shit about her and her kingdom.
I agree with you, since I think that Frosta and the rest of the Princesses should’ve had a more developed lore (and character) in the show.
(Not to talk about how they’ve changed Frosta’s personality radically, from “I don’t want to be treated like a child” to literally be a child, literally. I understand that it’s because she became pretty happy after she joined the Rebellion, but still, that was a very radical change done quite quickly, and don’t get me wrong, I adore Frosta and I liked her both when she was serious and when she was acting like a child, but still).
I understand that it’s because they had an episode limit and because they’ve focused on Adora and Catra, but still, they could’ve done more with the Princesses on the show, including Frosta.