I don't think you need to stop riding. USAFA has stables and some cadets bring their horses there. Demonstrating leadership with impact should be the goal. Sports are one path to that goal, but there are other ways you can accomplish this. If you stick with equestrian, you will need to find ways to explain your activities to a panel of people who do not know that world. Conversely, mainstream activities like "Cross Country Regional Qualifier" need little explanation to a panel of people who have never met you.
I am not of the belief that you must have sports on the resume. I am happy to be proven wrong about this, but my experience shows this is only one possible resume bullet for typical applicants. I didn't have a sports background, but I had a huge leadership resume across multiple organizations. As an ALO, I was assigned to only 1 school and pulled 4-5 students PER YEAR from that 1 school for multiple years. In those admissions cycles, we would have all kinds from mathletes, to band, to athletes. The whole person concept is what is important. Active students with solid leadership experiences across different organizations are the candidates who stood out. I do believe that recruited athletes have an easier admissions path, but that is not the norm. Most applicants are not recruited athletes. Simply having sports on the resume is not the golden ticket. Achievement and leadership are the underlying traits of successful candidates.
To be crystal clear - I am saying USAFA accepts students of varied backgrounds. A lack of activity in one area MUST BE OFFSET with activity in another area. If you are doing less in athletics, do more in service and leadership. If you are doing less in athletics, you really need to CRUSH the candidate fitness assessment to demonstrate physical aptitude for the challenge. If you are doing less in HS GPA, you really need to CRUSH the standardized entrance exam to demonstrate academic aptitude. If you are challenged and have constraints on the extra curricular activities you have access to, you need to find a way to demonstrate leadership and service.
Through your application process, you will be compared to others. You all have 24-hours in a day, but choose to spend those hours differently. Be prepared to explain how you spent your time, why you chose to spend it that way, and understand that in the end a panel of people you do not know will decide if it was enough.