winter road south

To be really "safe", I'd suggest 95 to I-10 west at Jacksonville.
January really isn't a good time to be sight-seeing in the mountains.

We take I-88 to I-81 every January on our way south and have never had a weather issue on the northern end that affected road conditions. We do pay attention to the weather forecasts before starting out, and adjust as needed. Only once have we stayed an extra day somewhere to wait out a storm so far, and that was in southern VA to avoid icy roads on I-77 in NC. We always include enough "flex time" in our travel plan to allow for unexpected delays while still meeting reservation deadlines on the other end.

Here in TN we rarely get "snowbound". Plus, if you are headed south, i'd un-winterize around VA or TN. Both states are fairly warm in the winter.

I would stay off 81, lots of mountains. We sometimes take 81 home in the spring. We need to return North next week and will stick to 95 when coming back in January. Usually warmer on the coast,
although we did hit a snowstorm on 95 one year. Learned never to get off 95 in North or South Carolina, they have no equipment in that area.

You could plan to take I-95 down to I-40, across to Nashville on I-40 to pick up the Natchez Trace Parkway, then US-61 down to Louisiana. These Interstates are kept clear all winter, in winter weather country, although there are sections of I-40 that get caught by road blockage disasters from time to time, but these are long term when they happen, so you'll know not to go that way.

I can't guarantee the parkway will be open all the way through, it is not miantained as a critcal thoroughfare, so if it gets buried under ice, it could be closed for a while.

You will not get out of subfreezing weather so fast that way. Nashville and south might be above freezing, more like around or below freezing, and I've gone through in snow and freezing rain more than once in January. I-20 is a safer winter route, as bad weather is more often just rain, although it might be close to freezing.

But your other requirements, getting out of freezing weather as quickly as possible, suggests I-95, or even US-17, as a route down, because the closer you are to the coast, the more likely ocean air masses will have pushed away colder air coming off the continent. The years I lived in the Carolinas, it would be wet, cold, but above freezing on the coast when US-301 (where I-95 now runs) was covered with ice or slick with refrozen snow. I-95 should be better now than 301 was then, because winter maintenance standards are now better, but you can still be in freezing air until well south of Atlanta, January through February. I've also gone through the area in January with temperatures in the high 40s to mid 50s, something that seldom happens west of the Appalachians north of I-20 corridor.

I almost always have lots of alternatives in mind for these trips that go from one corner of a rectangle to another, and make my choices last minute based on weather, short term forecasts or what's happening right now. Often a diagonal looks shortest, but it is not always the best, there are usually more possible diagonals, and following the sides, straight south then west, or west then south, seldom costs more than 10-15% extra miles, and less often, extra time.

Mountain Directory East might be of some help

I think you'll need to watch the forecast before finalizing your plans. Taking I-95S seems like the best bet at the start, but when/where to head west could depend on the weather. Lots of options from Virginia and further south.

Probably still early to plan. The weather here was weird last year, so at this time, its anybodys guess. For me, I would like to say come across Tennessee on I-40, then take the Trace down to Natchez. Usually it would be no problem. This year, who knows?? Keep your options open.

Allot of winter of late in that area! Ice today. Would go farther south! Find a more southern route and locate Motel-6 along the route as they acommodate dogs on a first floor. We have used them before when traveling without our TT across country.

I'd take I 95 down to I 20 then across to Atlanta. That gives you a couple of choices to go SE from there.