You definitely have a chance at vet school. I would advise against exclusively applying to Cornell because it’s essentially wasting money if you’re flat out rejected.
I do think getting equine and large animal experience is necessary because even if it’s not for you, you’re going to have to still work with those animals in vet school. Additionally, none of the options you have listed are extracurriculars, these should be clubs, or hobbies that you engage with to be a well rounded individual.