The preserve has no admission charge. Sea Pines, the gated community it sits inside, does charge non-residents to bring a vehicle through, and there is no way to walk around that.
How it works in practice. You buy a daily pass at either the Greenwood Gate on Greenwood Drive or the Ocean Gate off Cordillo Parkway, both of which sell passes through the day and into the evening. Recent published rates have been in the region of $10 for a standard two-axle vehicle, and rates change, so treat that as a band rather than a promise. Anyone staying inside Sea Pines already has a pass through their rental or hotel, and does not pay again.
Two things worth knowing. Day visitors are not permitted to enter Sea Pines by bicycle, so the plan of parking outside and riding in does not work. And one pass covers the whole community for the day, which changes the economics completely: the same ticket gets you Harbour Town and its lighthouse, the Stoney-Baynard Ruins, Lawton Stables and South Beach. Doing the preserve as a standalone errand is poor value. Doing it as the first stop of a full Sea Pines day is not.
Arrive early if you can. The gate queues on Greenwood Drive build through the middle of the day in summer and on tournament weekends in April.