There are a number of horse riding companies and centres on the Island that will provide you with all the advice and equipment you need for riding. As well as your trusty steed, it is a good idea to take a map of the trails, sun screen and comfortable clothing and footwear. It is important to always take some warm clothing with you as the temperature can drop significantly at higher altitudes.
You will also need body protection gear to ensure your safety during the ride, and don't forget to take something to eat and, most importantly, water.
Bear in mind that each person's needs may vary due to a number of factors, such as the duration and difficulty of the ride or the areas the trail crosses. The best thing to do is find out all you need to know in advance from the organisers.