We're in Zone 7a, so colder than you, but you could definitely grow chaya and moringa with winter protection.
Not to mention a zillion or so other amazingly nutritious and beneficial plant foods.
My dad was born and raised in Honey Grove, in Fannin County, which is about twenty miles due east of Paris, so a similar climate to yours.
And my eldest sister still lives in a Houston suburb.
This past winter was by far our warmest since we've been here, with a low temp of 14 degrees, but in the three previous years the low temp was minus 3. Brrrrrr.
Too cold for this Sunbelt kid. ;-)