Sedona (and nearby Cornville) is mild all year round. December/January is winter so nights will be cold and snow is possible, though rare and doesn't last long.
The Grand Canyon is almost 3,000 feet higher so severe winter weather potential is much greater. We don't advise chains. When storms come through up there, everything shuts down for a day or two until the storm passes and roads are cleared.
Use wunderground.com to search weather trends.
Cornville is near Cottonwood (I am sure you already know this). Typically, it does not snow here, and if it does, it sprinkles and has melted by high noon. Last year, we did get a cold snap which left snow on the ground for a week or two!
It does snow a little more frequently in Sedona.
It does snow a lot more at the Grand Canyon and if there is snow on the road, it is best to stay close to home because the vast majority of people driving on the road are ill equipped with summer tires which results in many cars being in the ditch or blocking the road.