January and February are ice and snow times for KY and TN. You'd probably have to go to at least northern GA to avoid the really bad weather. The mountains in northern TN on I-75 can be especially nasty and freezing rain is common in KY and TN at that time of year.
I store mine about 23 miles from my home. The storage lot is small but I've never had any problems there. It's just a parking space, no cover. They have open spots right now but they'll be full when fall arrives. It's stored in Georgetown, KY off I-75. Storage Rentals of America, Connector Rd, Georgetown, KY (formerly SPS storage). About $59 a month
In Louisville, KY off of I-64 heading to Lexington is a privately owned place with uncovered, covered and enclosed storage. I have no idea what they charge but it looks like a really nice place, just too far away for me.
Storage Solutions, Louisville, KY, Welcome
Here is what we came home to this past February 16, about 15". The storm was from northern KY to central TN.