Argh! How annoying. I can imagine this being common sense if this particular humane society's mission is to provide spay/neuter services, or this particular event was a spay/neuter fundraiser, but otherwise? Not exactly intuitive. (Also, was the woman's tone rude? I don't think it's particularly rude of her to explain that you couldn't participate. "It should be common sense" leaves something to be desired, but I'm not in favor of killing the messenger, so to speak.)
I'm with previous posters that you should call/write to the organizers. Because the money isn't an issue for you, I wouldn't mention that part. However, I do think you should explain what happened. Jayhawk has the right ideas. Focus on your expectation (that your pup could participate), the reality (that he couldn't), and your reaction (disappointment). If this is an organization that you typically support/like, then use the "sandwich technique." Start with something good, explain the problem, then end on a positive note. Something like this, maybe:
"Dear Awesome Organization,
I'm a huge supporter of your organization and mission to do good for our furry friends, so I was really excited to take part in your Halloween party. I made a costume for my puppy Shaman, and when I got to the party, we signed up and I paid the entry fee. We were about 10 minutes out when a staff member pulled me aside and told me that Shaman would not be able to participate in the contest. When I asked why, she told me that it was because he was unneutered and it sends the wrong message at a humane society event. I was very disappointed.
Money isn't the issue, since I support your cause and am happy to donate. However, I feel that the rules of the contest should have been clearly stated in promotional materials and on the entry form. I didn't think the altered-pets-only restriction was intuitive, especially because there were other events opened to intact animals.
Again, I love the work your organization does. However, I hope you take my feedback into consideration for future events. (Include the following only if it's true:) I'd love to participate in more of your activities, but it's important that I know whether or not Shaman will be welcome.
I think this gets the point across clearly and shouldn't make them defensive. You explain the problem and make a request.
Also, would you be willing to post a picture of Shaman in his costume? Pretty please with candy corn on top? (If you don't want to post it, would you PM me one?)