Katrina is a “blooming lass, plump as a partridge, ripe, melting, and rosy-cheeked” who is very light on her feet and enjoys romance.
To me, Katrina’s flirting is akin to Brom’s pranking:
Though Brom was much given to madcap pranks and practical jokes, there was no malice in his mischief. Indeed, with his waggish humor and prodigious strength, Brom Bones was quite the hero, all the country round.
Analogously, Katrina is the closest the county has to a princess, being the only child of the richest farmer. The men treat her like royalty by giving her attention, setting her picnic, and carrying her packages. She accepts their favours and sometimes gives individual attention, in a playful but not overly sensual way.
Though Katrina is flirty, she’s not overly seductive - in fact, Katrina has limits:
You can do more with [other girls] but Katrina will kiss and run, to her, a romance is fun with always another one to start.
Considering that “every part of the Katrina’s heart was jealously guarded by a host of rustic admirers,” (aka “simple country bumpkins” by Ichabod), she has to set boundaries and doesn’t give preferential treatment (unlike Ichabod with mothers who can cook). She has fun and she maintains her values.
Katrina doesn’t allow anything other than holding hands, dancing, or a chaste kiss on the hand. Also, considering she would be an heiress, she would need to be careful since men might only want her for her family farm, i.e. money.
Katrina can’t help it that men admire her nor does she seem to be resented by any other girls for this. I don’t find her spoiled or entitled because, on the flipside, she doesn’t mind if others get the spotlight. For example:
Ichabod showing off dance skills in his solo at her party
Ichabod as “man of the hour” with girls crowding him
Brom “dancing” with Tilda
Brom telling his story/song
Although she usually gets attention, she doesn’t mind if others get attention and rarely, if ever, does she show jealousy or envy. And so, overall, I find Katrina a confident and carefree gal.
…a confident and carefree gal with a mischievous side >:)
We already know she likes casual romance but, before the story takes place, the narration states:
The ease with which Brom cleared the field of rivals both piqued and provoked the fair Katrina. And she often wished that some champion would appear for once and take the field openly against the boisterous Brom.
In a way, Brom was not only impeding on her fun but also he didn’t have any real competition until Ichabod came. And once they started to compete, “Katrina  chose to stir the embers of the smouldering rivalry.”
This is partly due to her fun ways with romance but I believe it was also a way of her to see if Brom would havecompeted against a suitor who wouldn’t back down. Thus she used their rivalry to see if Brom really liked her - but, considering Brom’s history with his rivals, Katrina needed to encourage Ichabod a bit (=“Thus, one invitation in particular carried a most personal and provocative summons.”)
And so mischievous Katrina kept track of this rivalry with as much delight as the viewer, with particular attention to Brom’s reactions when Ichabod outdoes him:
Ichabod picks up her packages
Ichabod walks her from her horse
When Ichabod is inside her house
first, dancing with Ichabod and Brom is sitting on the bench
second, when Ichabod cuts in the dance and gets her back
(First, Brom falls over gate; Second, falls down outside) Both she and Ichabod see what’s going on
The only time Katrina checks on Ichabod is when he fell into the puddle and she gave him a handkerchief. She did also check on both of them from her window, right before Brom was going to punch Ichabod; perhaps her check to prevent the rivalry from going too far.
Overall, considering that Katrina has Brom on her mind more, I think she liked him more. And it makes sense that they marry. She’s fun-loving like Brom and her most joyful time is when she’s listening to his story, smiling and laughing. :D
Known for Katrina Van Tassel in Sleepy Hollow. Precocious, outspoken child-teen starlet of the 1990s. She made her screen debut at the age of 9 in Mermaids(1990), in which she worked with Winona Ryder and Cher…