My genre of choice is historical novels set in the Medieval period. I know of one historical figure in particular that can be interesting for you:
1. Jeanne de Flandre (14th cent.)
Wife of Jean de Monfort and mother of his only male heir. In 1341, Jean de Monfort was a claimant to the Duchy of Brittany against Charles de Blois, nephew of the French King. Jean de Monfort was imprisoned by the King and his wife acted as his representant, rallying an army against Charles de Blois and capturing an enemy town. When her stronghold of Hennebont was under siege, she donned armour and led 300 men in a successful attack, then went on to gather reinforcements before returning to her castle through the siege.
Note that she acted as a regent of sorts: she was defending her husband's and her son's rights. It was under that banner that the men obeyed her orders and followed her lead (although they must have recognised her value as a strategist and effective leader in battle, otherwise they wouldn't have followed her).
I know of several historical figures who acted as head of the family, either because they were widows or because their husbands were at war and they must organise the family estate. For some powerful families, this required a lot of cunning and, occasionally, organising the defenses of a stronghold.
Elvira of Castille, Countess of Toulouse, is an example of a woman who accompanied her husband in a crusade (12th century), standing by his side through a siege and through a pregnancy.
Such examples lead me to believe that for a princess to act as an army leader would be uncommon but not impossible.
First of all, there must be no male above her to shadow her. If there are no male heirs, for example, then the army will have to accept her as their leader. One could imagine the king recognising her abilities and sending her off with a group of men in order to gain experience. In this scenario, she should act the way a male would while respecting dress-codes most of the time. In the heat of the battle, she'd naturally have to don armour... which would be male in shape, since those were the only types being made.
Naturally, she'd have an older man acting as a mentor-chaperone, and she'd still have a (very small) group of ladies-in-waiting to serve her in her tent.
While the king is alive, I doubt anyone would take her serious on her own, without royal backing. Once the king died, the counselors would start looking for a suitable suitor. Naturally, she'd have the last word (though it wouldn't be wise to go against the Council, not unless there were plenty of nobles backing her alternative choice. Even kings can get in a civil war if they choose their brides against the Council (and their subdits)).
Suitors would be chosen based on politics, not finer feelings (though one can always try to have both). I doubt she'd fight them, though. The natural thing to do would be to have a champion to fight in her stead. In such a scenario as I set up, one wouldn't endanger the future queen lightly. Anyway, what would be the objective of such a physical fight? If she is cold-headed and her strategic prowess is respected, then she'll know how to maneuver her allies into supporting her choice.
There's another scenario possible: the princess is not the heir, as her brother is next in line. But say that both the king and the prince like her military vein and support her endeavours. A strategic mind and manly bravery will win the army's respect (well, most of it), and anyone who disapproves of it will swallow their opinions to avoid displeasing the king and the prince (well, except for the priests, they'll complain loud and clear).
In this second scenario, she'll have much less power when it comes to suitors. She'll have to bow her head to her father and brother's wishes... or have enough cunning to maneuver them (meaning, getting enough powerful allies to support her choice).
A note concerning the word 'princess'. In the 14th century in the Iberian Peninsula, the kings called themselves 'principes', or princes. They meant that they (and all other kings, naturally) were the 'principal people' of the world. There wasn't yet a feminine counterpart for 'principes'.
A princess of the time had nothing to do with "princessy". They might be rich, they might be spoilt, but their lives were harsh nonetheless, and they must be cunning if they have any ambition. In the 14th century in the Iberian Peninsula, Kings, Queens and their heirs would often travel throughout the country, sometimes spending the night (or a few weeks-months) in a royal castle, but often spending time in other castles or even in small villages... with less than ideal conditions.