When you are planning what trees to plant near your pool keep in mind what type of foliage they have. Some types of trees offer you a great deal of natural share areas, but keep in mind that will also cool the temperature of the pool off if it covers the pool for several sun hours of the day. Some shade trees also offer you great looking foliage in the warm summer months, but in the spring and fall they can be messy leaving leaves all around and in the pool if not covered. Also keep in mind that the larger trees also have larger root balls and they can often extend out to far reaching areas. So unless you want to consistently clean your pool and have leaves in it, I would guide you away from any type of leaf bearing trees.
I would however recommend smaller shrub type trees to go around the far edges of the pools. They can add amazing color and are relatively low maintenance and easy to maintain. They also offer smaller root balls so no need to wonder if in 10 years the root will be disturbing the pool plaster or concrete area. They also require less water than larger trees, so you can conserve more water and spend less time watering the trees, and more time enjoying your pool!
If you are still unsure what type of trees you should plant around your pool then contact your local landscape company and they are sure to have many good ideas for you!