“The nerve of him!” the young woman cried, flinging her arms into the air as she stormed into the barn. Her friend was grooming her horse diligently and happily.

Her name was Ladimira. Lithe and nimble described her best; she was tall and thin, almost nymph-like in build. Her dancing eyes shined green and happy, despite the reoccurring frustration with her father. She wrapped her golden hair up in a ball and held it at the back of her head for a moment before letting the long, curly locks fall back to her shoulders with a sigh.

No need to stop the action to introduce a character. You can simply write something like:

Ladimira leaned against the stable wall, crossing her arms, waiting for her friend to pay her some attention. She tossed her long golden hair over her shoulders with a sigh, hoping her frustration would garner her sympathy.

In addition, you must choose POV. Make sure you note the difference between 3rd Person Limited and Omniscient. If you're using 3PL, you can't write a line like:

Her dancing eyes shined green and happy, despite the reoccurring frustration with her father.

The reason is Ladimira can't see her own eyes, unless she's looking in a mirror. The best analogy I can use for 3PL is to imagine placing a movie camera directly behind the eyes of a main character. The technique allows the reader to become that main character and experience the story through his/her eyes.

Omniscient is an all-seeing narrator, as if "God" were telling the story. But a warning. Any story written in omniscient risks the threat of losing intimacy with the reader. In a sense, it automatically makes it so the reader is being "told" the story, rather than "experience" it. (Ever heard the expression show ,don't tell?)

Her friend laughed. It was a melodious laugh, full of spirit and frivolity. Kassandra was a brilliant girl: quick of mind, strong of heart. She was pretty, with a light build and soft olive skin, and pretty, blue eyes to match, too. Her hair was a rich chestnut color, cropped short above her ears. It was not, by any means, a popular fashion amongst women, but it was certainly quite becoming all the same.

Same issue as I've mentioned.

“Actually, my mother had a marriage arranged for me, when I was about three years of age. His name was Ruhevirre.” She made a face. “A good for nothing, he was. He refused to engage himself in sports or in horseback riding; he said that he did not like sports and that the horses frightened him.”

Because I don't know the character of Kassandra (or Ladimira for that matter) yet, there's too much detail in the dialogue for me to read every word. I would be tempted to skim this.

The women rolled their eyes, smiling, and closed up the stall doors.

Feels like a camera shift rather than a scene break. The subject's not concluded.

On their way back up to the house, they paused and curtsied respectfully as Ladimira’s father passed by. “Good morning, girls.” He gazed hard at his daughter, but his tone was light and airy. “Good morning, Sir,” Kassandra replied politely. After all, Lord Trenald and his wife had taken her in as a child; paying her respects was the least she could do. Ladimira met her father’s gaze with one just as cold. “Good morning, Father.” Lord Trenald nodded and continued on his way, pausing only once to glance back at his daughter. When he was out of earshot, Ladimira sighed. “It is almost like he wishes I was a son or something,” she told her friend.

This feels choreographed like a film. It's giving motives behind each character as they interact. This doesn't work well in fiction. In a script, you'd have a character go:

TRENALD (light,airy): Good morning, girls.

KASSANDRA (politely): Good morning, Sir

Kassandra tapers her smile, trying to remain couth.

LADIMIRA (coldly): Good morning, Father...

INSERT: Trenald narrows his eyes and glances back at Ladimira.

CLOSEUP: Ladimira sighs. She leans her cheek to Kassandra's ear.

LADIMIRA (scathingly): It's almost like he wishes I was a son or something.

But in fiction, this type of choreography is not necessary. Actually, it's arguably improper. The reason is because you don't have a camera. Instead, you've got to generate a camera image inside the reader's mind. (not the author's, but the reader's). So your camera becomes your POV... which means, use the emotion and thoughts of a character so that the reader understands the hostility behind Ladimira's interaction with her father. Then the reader will SEE/FEEL what you (the author) want them to.

“Come on,” Kassandra continued, grinning. “Let us skip embroidering and find something to eat.” “Great idea.”

Again, didn't feel like a natural scene break.

That night, Kassandra sat near the window in the room she shared with her friend. Lord Trenald had called his daughter downstairs to ‘have a talk’ with him. So now, Kassandra was left to herself, and she passed the time staring out the window. The stars were shining, she saw, and the moon was full and bright tonight. Everything seemed calm. Or at least it would have, had she not heard the shouting from downstairs and the footsteps stomping just outside the bedroom door.

Better. You've got one character and someone a reader can begin to get behind. However, you've got passive voice and remote narration. Passive voice is any time you use a variation of "is" as your verb. Remote narration is when the language is bordering an omniscient POV, making us feel as if it is being told from afar rather than experiencing it.

Take a sentence like this:

So now, Kassandra was left to herself, and she passed the time staring out the window.

What if it looked like this?

Now alone, Kassandra passed her time staring out the window.

*Also, I noted that this scene (Ladimira reenters and they escape out the window) is written much better than the sequences preceding it.

“Bandits!” An arrow sliced through the air, coming dangerously close to Kassandra’s head. “Run!”

The transition to this action scene feels abrupt. I'd want to see them scurrying out into the wilderness before the attack.

...but it's interesting.

Ladimira cursed the bandits inwardly. Of all the things to happen!

POV break.

Nevertheless, one struck Ladimira in the back, near her shoulder.

The writing here doesn't seem to exhibit enough emotion or peril. It seems to just "tell us" that this happened. Well, I like Kassandra more than Ladimira at this point anyway, but still I'd like to feel Kassandra's terror at seeing her friend being struck by an arrow. Some feeling of oh no! She's been hit! I could be next! That terror of oh-my-gosh-my-best-friend-may-be-dying and oh-crap-do-I-leave-the-injured-and-save-myself can somehow be exhibited to intensify the experience.

for fear of falling.

Another POV break.

Whoever they were, they must not have had horses, or the chase would still be on.

Who is thinking this?

“I know,” she said sympathetically.

Don't use adverbs. Let the dialogue alone allow the reader to infer tone.

A rough voice answered, “Foe.”

Good hook!

Anna, I think you've got a moderately good start, but I recommend choosing a POV and sticking with it. Kassandra is my choice, but it's your novel, so it's your choice. You've got a few elements in the beginning that don't seem necessary to me. I have read your prologue and agree with Amber Lynn's sentiments-- I didn't see the point or understand what was happening. But I get more a sense of story in this chapter, and I can imagine it going somewhere. Your story description doesn't allow me to know more about what this novel is about, like say the back of a book cover might entice me to buy it. I think you can do some more with these characters in Chapter 1 to get us more interested in them, however. At all costs, I recommend trying not to think of it like a movie playing in your head. Try to think of your main character, what she's experiencing and what she's feeling, and tell the story through that.

Best of luck.

 It's an interesting runaway tale, but I'm left wondering as to the intention. She and her friend run away, but I can't discern any compelling reason to sympathize with their decision to do so. I mean, I've read it over several times, but I just don't see why they run off. For adventure, perhaps, but... it leaves me hoping to see some larger payoff, something that will justify reading further. 

There is an implication that she's not at all happy about being used as a pawn in a larger game, but there is no background to her character that makes it such an imposition on her, imposition enough to make her escalate from speaking poorly of her father to then running off.

Would a Lady-in-Training speak thusly? She's been raised in a court, her whole life has been dedicated to precisely one end; was there an event that caused her to choose to rebel against the norms? Why does she so easily call her father a "git," and why does her friend not find that shocking?

Where in their training (hinted at by the reference to embroidery) do they learn to tack and harness horses? To ride without escort? I am assuming that this is some manner of medieval world, of course. They seek adventure as a break from their routine, an escape, if only temporarily, from their assumed destinies - did they pack well, or is that one of the challenges of the tale?

Yes, I'm being nitpicky. It's a well-written start, but it feels shallow, I guess that's what I've been trying to say. I wish there was more backstory, or suggestions thereof, that make me sympathize with the heroines.

Upon one more reading, there is something that stands out: There are no contractions in their speech! I don't know if this is intended to convey a sense of place, but it reads very stiltedly, uncomfortably. The friends do not implement contractions when they are speaking? Can not one assume that a dialog between friends, especially an intimate conversation involving running away, would be done with the most shorthanded of speech forms, to show how close the friends are in their thinking? They have a history, they've grown up together - I've found it hard to be sympathetic because they speak as though they were ambassadors from distant nations.

All that said, keep writing. Stories like this are always entertaining, and I think you have a thread to a larger tapestry.