I went to undergrad at University of Miami so the majority of my vet/animal experiences were in the Miami area. There are some opportunities out in 'horse country' i.e. some riding institutions like Huntinghorn Stables that will take volunteers. Mind you it is not vet experience, but they periodically have a vet who comes in to see the horses and you can state in your application that you witnessed certain procedures during your time volunteering there. There are also opportunities in Homestead, but you have to be willing to make the ride out there.
My strongest equine experience was during one of my spring breaks - I just took a trip for a week and spent time in Ocala, FL. There are horses everywhere, and it can be a relatively cheap trip as certain places who regularly take student volunteers will supply cheap housing. If you really want horse experience and can take the time out, it is worth it.
Honestly the great thing about Miami is that we have access to several species/places that many applicants outside of Florida do not. Try to get experience at Monkey Jungle, Parrot Jungle Island, Miami MetroZoo, Seaquarium, etc. I was asked why I did not have food animal experience during one of my interviews, but I answered honestly saying that there weren't many opportunities for it in Miami but I accumulated experiences in almost every other possible discipline available. I was accepted there.
That being said, I agree with hellokitty89 - Use the diversity available in Miami to your advantage, and don't stress about not having a lot of horse experience. If you can rack up a few hours here and there, great, but there is so much more out there that I feel it is not 100% necessary for a strong application.
Good luck!