Turns out when they made the text strings for the horses, they did make them compatible with the chooseable pronouns!
As an example, this is what a text string for one of the horses skill text's looks like
{0.SimFirstName}'s new Skill in Endurance will begin to help {0.SimPronounObjective} manage Fatigue better. As this Skill increases, {0.SimPronounSubjective} will also perform better at certain Community Jobs and the Endurance Race, Show Jumping, and Ultimate Horse Championship competitions.\n\nTo track Horse Skill progress, select "Open Profile" on {0.SimFirstName} in the Relationships Panel.
Therefore, it is clear that the horses are designed to have this pronoun feature.
