Patrick's suggestions sound reasonable.
Most crossings of the Rockies in winter would not be something I'd attempt, so using a southern route in the west seems like the obvious answer. I think that I'd start in the west on or near the ST, then head northward as I got further east, that way you'd cross the Appalachians a little later. I'd be flexible about the route and decide where to head north based on how the weather forecast looked at the time.

If the forecasts at the time were terrible you could stay south longer. If they looked better you could head north sooner and more aggressively.

There will be a chance of freezing temperatures and snow even on the ST and the further north the bigger those chances. Personally I don't mind overnight freezes with cool daytime highs or even snow, if the roads are clear in a day or two, but the chance of real cold and lasting snow and ice is not something I'd want to deal with on tour.

I personally wouldn't consider riding the TA west of Pueblo anywhere near as early as a February start in the east would get me there. I assume that the WE and the NT would be similarly a problem.