I don't understand the question.
Here in Ohio, bow season is not called "primitive season". It's called archery season. It usually goes from the beginning of October until the end of January. Longbows, crossbows, compound longbows are all allowed during "shotgun/handgun/muzzleloader season" which is either one or two weeks during the end of November into the mid of December.
Then we have "primitive season". It's muzzleloader only for guns. But bows are allowed during all of our gun seasons. The only requirement is that you wear hunter orange during any deer gun season no matter the weapon carried. But that goes for any type of hunting during any of our gun seasons. Say you want to coyote hunt during shotgun/handgun/smokepole season, you must wear hunter orange.
So, yes. Crossbows are allowed from beginning of October to end of January. But I don't understand how Florida could call bow season "primitive season".