Seminoles aren't even native to Florida. The tribes in Florida when the Spanish first arrived were the Apalachee, Timucuan, and Calusa (along with some smaller groups). They were mostly wiped out by European diseases. Seminoles began as a branch of the Creek tribe, their name means runaway. They developed a new tribe that migrated into Florida around the time of the Revolutionary War. By then, St. Augustine had already been a city for 200 years. They primarily used muskets and metal hatchets, not bows and arrows, stone tomahawks, or flaming spears. They also generally wore clothes made of cotton fabric. Chief Osceola was born Billy Powell, more European DNA in him than Native. His mom was named Polly and his dad was named William. They were not great horsemen like the Plains Indians and certainly didn't have the Appaloosas of the Pacific Northwest.
FSU has gotten more historical over the years. Initially, they just used a stereotypical Plains Indian, "Sammy Seminole". Their "Chief Osceola" character has evolved to be a little more accurate, and they recently asked their fans to not show up to games in feathered headresses.
The Seminole Tribe consists of real people with a real history--a fascinating and compelling history (until you get to the last few years and the casinos). If you are going to call yourselves the Seminoles, then try to honor that history. I'd prefer an authentically dressed Seminole carrying a musket than a guy on a horse that never existed in Florida carrying a flaming spear.
Here are some historical photos of real Seminoles (most of these look to be late 1800's early 1900's):
Alex.