This time of year your best odds at avoiding snow is the I-10 route, I-40 is more of a maybe (but my preferred route), Flagstaff is almost a guaranteed snow area but you get thru quickly. I-80 across Nevada can get sketchy this time of year, and the Donner Pass frequently gets shut down to those with snow chains and 4wd only. If you watch the weather and time it right, you can probably make the trip without driving thru snow.
Couple years ago it started snowing heavy one night, cars and trucks south of town had to come to a stop, next morning emergency crews had to rescue drivers by digging them out of 6' snow, 2 days later they were able to drive the cars out. Standard rule here for winter driving is always carry some food, water, blankets and some tea light candles, the candles will provide enough warmth inside a vehicle to keep you from freezing, just make sure to crack a window so you don't die from CO poisoning. And idling a vehicle buried in snow WILL kill you.