Riding the whole ST in winter is possible with some chance of snow delays. I started in San Diego in mid February and finished in Pensacola in Mid March. I had decent weather the whole way. I only saw a little snow on the roadside on the top of a couple passes and none on the road. Locals said the previous year I'd have had a few days of delay due to snow. There was frost a lot of nights, but most days quickly warmed to at least 50 and usually warmer. Basically it was pretty nice. It got really cold only one night (18F on my thermometer).
In December I'd expect similar temps, but much shorter days. Check weatherspark to be sure. I chose Spring for the longer daylight hours.