"This student loves her horse."
Translation:Эта студентка любит свою лошадь.
To quote RussianLessons.net "The Russian pronoun “Свой” means “one’s own”. It replaces the normal possessive pronoun when it refers to the subject. Unlike English, in Russian the reflexive is required in the 3rd person. If you were to use the normal possessive pronoun it would indicate the dog belongs to someone else. It is optional in the 1st and 2nd person but normally used if the subject is “Ты”."
I believe it should be accepted. However, please note that your translation would mean that the student loves a horse that belongs to some other woman. If you meant to say that the student loves her own horse you need to use 'свою' because the subject and the pronoun would refer to the same person.
Would это студент любит её лошадь work if it is the case that a male student likes someone else's horse (and that someone else is female)?
I can see why this isn't accepted, since generally speaking, the "this student" and "her" would be assumed to be the same person, but would the above Russian sentence work for the scenario I just said? Would there be some other preferred way of saying it instead? Thanks!
Why do you expect it to be genitive? Because of её? её is unconjugated for case, so it won't give any hints to the case of what it is modifying.
It should be accusative as любить is taking the horse as the direct object with её modifying horse/лошадь to indicate possession. The accusative case is why the given solution "Эта ученица любит своего коня." has коня, the accusative form of конь. Note also своего, which is the animate accusative form of свой for modifying the accusative form of horse..
The form of the pronoun is determined by the object, not by the subject (though "лошадь" is feminine just like "студентка"). "Свою лошадь" is an accusative case (for animate objects).
Эта студентка любит свою лошадь.
Эта студентка любит своего коня.
Этот студент любит свою лошадь.
Этот студент любит своего коня.
The last two examples won't be accepted here because the English sentence has "her horse".