"Can you see her horse?"
Translation:Vidíš jejího koně?
This is the accusative case, as you surely know. The pronoun "její" looks the same in accusative ("její") except in the masculine animate gender, where it's "jejího". And since "kůň" is masculine animate, that's the form you need. You can check out the declension table here: https://en.wiktionary.org/wiki/jej%C3%AD
The forms are the same as the forms of soft adjectives (like "zvláštní"), by the way.
Also notice that "Vidíš její koně?" means "Can you see her horses?" (plural)