I am trying to find a grant to help me pay for a horse riding arena to hold horse shows, lessons, rodeos and other activities for my community?

So have you hired a professional grant writer to submit it to many of the private companies, Have you set up a Arena group, got incorporated, normally as a non profit.
Have you started fund raising, since even with Grants you will normally have to come up with about 1/2 of the costs plus have to have about a year of operating costs on hand.

Most grants come from private business, firms like Walmart, Home Depo and more.

You would do well and have a better chance of getting grant money if you include ideas to help the disabled and underprivileged with riding and equine care.

And also have you approached over area civic groups, the city and the county for assistance