In the past I've used Weather.com to monitor weather forecasts for cities along our route from MI to FL: I-65, Indianapolis, Louisville, Nashville, and Montgomery, AL. I also watch our destination, Crystal River, FL. I check these locations weeks in advance almost daily and watch for a stable weather trend.
We have used a "window period" for our departure date. For example if we wanted to be at our destination on January 1 I'd be looking for dates from December 25 to December 28/29. One time a few years ago I saw the weather changing on December 27 in SW MI so we left on the 26th. If you try to pick a specific date rather than a window period you may get caught up in a weather condition that isn't good.
Also, if you think you will just wait out the bad weather you might wait a lot longer than you had planned.
We now leave MI after Thanksgiving to avoid the after Christmas period and have had great weather conditions the past two years.