Crown Duel and Court Duel by Sherwood Smith
Meliara is the heiress of the County of Tlanth. Her father's deathbed wish is that she and her brother Branaric stop the king from breaking the Covenant with the Hill Folk and take the throne themselves. They gather a small army to attempt just that, and they are more successful than they'd expected to be until the Marquis of Shevraeth joins the fray.
The Covenant is that they won't cut down trees for wood, and that the Hill Folk will provide magic fire sticks to keep people warm during winter and fuel their stoves, etc.
Meliara is sixteen, and she is impetuous, impulsive, and has a chip on her shoulder the size of a castle. Her mother was murdered (by the King) when Mel was six, and Mel was never given lessons in being a Proper Lady. She hates courtiers and thinks they're all ridiculous. But after the king is deposed at the end of the first book, Bran moves to the capital and meets a lady to marry, while Mel sets about restoring the keep at Tlanth. They come to Tlanth to persuade Mel to come to the capital.
She receives a mysterious gift on her birthday, and she doesn't know who it's from, but I did. She begins a letter exchange with the mystery person, and it turns into a courtship. The revelation of the mystery person is actually really cute, even if I knew the whole time who it was and was just waiting for it. It's shy and sweet.
In the first book, Mel is extremely grating and irritating, because she just reacts without thinking--impetuously. But she's sixteen; I probably wasn't any better at that age. I wanted to shake some sense into her. By the end of the first book, she's started to realize that it's a problem, and throughout the second book she starts working to correct her mistakes. So she gets better!
Despite finding the protagonist irritating, I plowed through the first book in an evening, and the second one about the same. They're only around 200 pages each.
If you like YA coming of age stories and fantasy, horses and swordfights and magic, fancy dresses and banquets and balls, you might like this, too.