The NCEA stands for the National Collegiate Equestrian Association. There are 18 universities in the United States that hold Division 1 equestrian teams. A total of 270 scholarships are offered in Division 1 equestrian. Colleges with the most notable equestrian teams and programs, are Centenary University, Auburn University, Brown University, College of Charleston, Cornell University, University of Georgia, and more. Many colleges will allow you to bring your own horse with you, however, some require that you ride a horse owned by the university.
Here is a photo of the equestrian facility at College of Charleston in South Carolina.
Below is an informational video on recruitment for equestrians for college.