I'm about as south as you can get (outside of FL), and I've hunted rabbits all my life.
I'll tell it the way it was explained to me by Dad:
Prior to a "heavy frost," you need to NOT hunt rabbits–– even if the season has come in. This is because the rabbits (and squirrels for that matter) have "Wolves" in their skin that can go into the muscle tissue (I think).
"Wolves" are a maggot-like worm that forms a cyst in the tissue about the size of a nickel. You really don't want to eat the meat while they have those. I've killed both squirrels and rabbits that I've had to discard due to having wolves–– even after a frost (that wasn't heavy enough.)
I've been told that deer get these too, but (due to the time the season comes in) I've never personally encountered them.