I'm in Central Mississippi, too. Yesterday, I rode in shorts and a Tshirt. Last week, I broke out the Jeans, gloves, beanie, and ym Great Grandpa's ARMY jacket.
I usually walk them down while I'm still on for 20 mins, unsaddle, put tack away while they are tied to the trailer, and then handwalk until all the sweat under the saddle is dry.
I've never had problems with my routine, and as soon as my horse is dry and stopped breathing hard, he rolls, gets a sip of water if he wants to, and meets me at the barn for his supper.
Cheyenne, QH Paint Trail Mare. Happy Trails, Y'all! Twister, Appaloosa Barrel Horse. Turn 'n Burn! These 2 horses stole my Heart!