Probably should also check the rules and regs at the place you're storing. That may be your answer right there.
We're in West TN, which is milder that you are. Plus we store at home. If the overnight temps drop below 32 degrees, but then warm up in the morning, you're most likely fine. Much longer than that, I would say winterize and then re-do it if you decide to venture out. We're getting ready to winterize even though is was an awesome 71 degrees here today - convertible top down day. But this time of the year you don't know from one weekend to the other and we have a mile long list of To-Do's, so we're calling it quits. Darn, hate that! But if you get out again, enjoy!