Nice pointers here! I grew up in Upstate NY and played college ball in the northern Midwest were it was always VERY cold in the early spring. Don't miss those February double headers in college when I wasn't pitching :-)
I definitely recommend wearing sleeves to keep the arm warm. A compression sleeve, such as Under Armour Cold Gear, is a good option because it's close-fitting and provides less wind resistance than a looser-fitting sleeve. Also tends to wick away sweat and keep you drier than cotton. Drier in cold weather = warmer.
It's also perfectly OK and recommended to wear a jacket (and gloves) before and after throwing, but do take the jacket off for the 20 or 30 minutes that you're actually throwing (long toss, bullpen, etc.). The thought behind that is practice how you play - you can't wear jackets in games, so don't wear it when you're practicing pitching.
I envy all you players and parents who live and play ball in the South!!