Are cover letters for small non-profit internships different from those for other fields?

I think you should write something that tells how the founder is your role model. The more specific you can be, the better. That said, I wouldn't make it long. Say something meaningful, talk about what you can offer, like that you're hardworking, have a passion for the mission, have studied the subject, things like that. If you have any experience raising money, like in a walk-a-thon or for a charity, mention it, as organizations always need help raising funds.