Umm... no they don't.
* https://en.m.wikipedia.org/wiki/Gun_laws_in_Arizona
As two quick examples check out the open carry laws in Texas and Arizona where registered personally owned firearms per capita is among the highest in the country.
A more correct restatement of your claim might be that "many" Southerners openly carry, but that's still a minority of a minority given that, per capita, most Southerners don't even own a gun. "Almost everyone" is reaching into some kind of weird libertarian wild-west fantasy stereotype.