Do you need to bring your own saddle and everything or do those come with the horses?
Cacowgirl had a good idea. Have you checked with the folks to see exactly what they recommend?
Anyway, just for yourself, I strongly suggest a hat with at least a 4 inch brim to keep your face and neck shaded from the sun. Long sleeved shirts, and comfortable jeans to ride in. I like light colored cotton buttonup shirts over the top of a tight cotton t-shirt, it's a lot cooler than a tank top or anything like that.
Slick soled boots that are comfortable for riding and standing/walking as well. I'm not sure what the weather is like there (I would imagine that it would still get pretty cool at night even in the summer), but you might think about taking a jacket as well.
Beyond that, I'm not sure what you might need to bring as I don't know what they might already be furnishing.