I've never done this whole BBQ Carry thing before,
I have, and allow me to share a bit.
Classically, a person with "a spread" wants to celebrate something--a windfall, a personal success, or perhaps a matriculation of some sort. Being a generous and gregarious sort, this person will know a couple hundred folk to invite to such an event.
The host will typically dress as they would for any other day "on the spread" (which might be also called "out to the farm" or "over to the ranch" or the like). Which would include the ability to cope with pest and annoyances (like coyotes).
In days of old, such a person would generally be acquainted of the Sheriff, the DA, and the like, and might well have access to Trusty's at the Jail who would hand-tool leather. Or, perhaps they knew an artisan who made up their tack. Really didn't matter, it was their land, so they could Open Carry whatever they wanted to.
Now, the townfolk invited to such things might be of similar stature, equipment and experience. Or, the town Pharmacist might just want to show off his fancy rig. So, it could be a social appearance as much as anything else. Now, note, all hands are polite, too. There's no onus for not being armed, or for perhaps toting something in pot metal (unless one were under a delusion it was Adamantium or the like).
Food would be "ranch sized," an entire side of beef sometimes. Pit smoking in the Barbacoa style is frequent. Emptying out the smoke house pretty common, too. There's a recent trend to hire in a "chuckwagon" with appropriate chefs to cater such things, too. "Pot luck" style is less common, but not uncommon.
At the core it's about community and generosity--if with a bit of pomp after a fashion.