People are recommending Kentucky and Virginia, but my daughter in Nashville was buried in snow (snow emergency shut downs) before the end of December at least twice in the past five years, and last time I went through Virginia between Christmas and New Year's I was driving through snow. My last trip through Kentucky, it was snowing from Bowling Green through Louisville to Cincinnati, and I got stopped by ice covered roads just north of there.
To be relatively sure to avoid snow (and the ice storms more common across the middle South) late December and into January, I would stop somewhere south of Interstate 20. Make that Interstate 10 if west of the Mississippi, because north Texas can also get buried in snow well south of Dallas-Fort Worth, as I've been caught in a Christmas snow storm in northern Texas twice in the past 12 years.
On the other hand, I've made many Christmas trips to southeastern and south central Michigan in the past 33 years, encountering no snow anywhere along the way. But that's variable, and not predictable over much more than a week. Other trips through that area I've been shut in for a day or two by winter storms across Missouri and Illinois, and across Tennessee, Arkansas, Georgia, Alabama, and Mississippi on Christmas trips to North Carolina.
Even Kalamazoo may not be snowy at the end of the year, but I would not count on that because of the lake effect snow reaching that far.