Ask Mr. Smarty Plants

The first place to go to find a list of potential groundcover plants for around your pool is our Native Plant Database.  Finding native plants that can be walked upon with any frequency is going to be a big challenge though.
Use the Combination Search feature instead of Recommended Species. This will provide a bigger selection with much more choice to narrow down. The volunteers and staff at the Wildflower Center who maintain the database have partners in different regions to help with these recommended species lists based on what is easy to access in local nurseries.
Under Combination Search, select the following categories: Florida, Habit (herb for herbaceous), Duration –Perennial, Light Requirement – Sun, Leaf Retention – Evergreen, and Height Specifics ( 0-1 ft.). You can narrow down this search further by indicating blooming time and color, soil moisture (dry, moist or wet).
Follow each plant link to our webpage for that plant to learn its growing conditions, bloom time, etc. At the bottom of each plant webpage, under Additional Resources, there is a link to the USDA webpage for that plant. Take a look there for more specific details about suitability before you put them on your final planting list. Think about including plants that have interest during a variety of seasons and that have more than one attractive feature (flower, fruit, foliage, etc.) so you can get more benefits out of fewer plants. 
This search resulted in 5 plants:

Antennaria plantaginifolia (plantain-leaf pussytoes) A low, colony forming plant with basal leaves and crowded flowers heads that look like cat paws. May grow better with a little shade.

Asplenium trichomanes (maidenhair spleenwort) A short, evergreen fern. Prefers moist conditions.

Callirhoe involucrata (winecup) Purple, cup shaped blooms in the spring and early summer.  Plant sprawls along the ground. Very drought tolerant and needs well-drained soil.  May go dormant in the summer. Prolong the growing season by deadheading the spent flowers before seed forms.

Callirhoe involucrata var lineariloba (poppy mallow) White or white with pink streaked flowers in spring. The trailing form would work well as a groundcover. Very drought tolerant.

Coreopsis lanceolata (lanceleaf coreopsis) Very drought tolerant. Spreads by self seeding. Deadhead to prolong the blooming into summer.