The best riding in AZ is in the mountains, and we do actually experience winter here, including snow.
We have been fortunate with temps in the high 50s and mid 60s for the last week, but there is still snow in the shady spots along our local twisty road. Just be advised it is possible to run into bike stopping weather.
Just watch the forecasts carefully, and be prepared to re-route (which may entail lots of straight and flat).
Same here in New Mexico. The mountain roads are snowed and iced in places. I just came back from a ride to Big Bend, TX where the weather and roads were nice. On the way down, however, it was super-slab all the way with heated gear on most of the time. A week ago I tried to take a shortcut through some of the low mountains southeast of Albuquerque, but got stopped by snow. Super-slab was the only option, but parts of it had ice patches (likely gone by now).
Winter storms come and go in these parts. In the winter I can usually ride around town if there hasn't been a storm in the past few days, but the mountains and hence the good riding, is off. Even if the roads don't have snow it will be cold, and they put so much gravel on the roads that it's not as much fun to ride.
If I were you I'd skip Arizona or New Mexico for the winter and fly down to southern TX or LA.
