4-H has a handbook, you might be able to find it online. It outlines what can and cannot be shown.
I grew up in the Adirondacks of NY, and EVERY county fair had horned cattle being shown by 4-H kids. But!!! Sometimes 4-H leaders make up their own "rules" for what can be shown, which is why I stopped participating in a particular 4-H club. The leader told me that my daughter could not show her Brahma calf, or ANY of our Dexters, polled or horned. That was complete BS - both breeds are allowed to be shown by 4-H youth, but he just didn't want them to be for some reason. After speaking with other parents at a Dexter show, I found out it is VERY common for 4-H leaders to discriminate against certain breeds. Some parents have fought back and been successful, but you have to wonder how awkward you might cause the situation to be if it is a small club (ours had about 10 members, which is why we left...).