Depending on what you end up doing, your services could partially fall into the category of agritourism. Since your idea seems to be based on the idea of recreation (in a rural area) without a tie to agriculture, the benefits of even loosely "branding" the enterprise as an agritourism attration would probably be minimal. I think you might be leading toward something more specialized than general agritourism. I think you are wise to be under the advise of your professional advisors. The non-profit route may or may not be the way to go, unless it would allow you to access additional funding.
You might want to carefully consider the specific focus of your business idea. Is the demand there to focus on only verterans? What would the demand be for this type of access to your property overall? Would a more open access facility allow you to generate more income to enable you to provide better services for veterans?
I would also encourage you to develop a business plan for the potential enterprise. This will allow you to better anylize the risks and opportunities associated with the idea. It will also give you a chance to figure out how much it might cost to do this and what fees and other fund raising levels would be necessary to make things work.
Sounds like a neat idea. Good Luck!