i have driven out to southern california to desert race the last 4 years. Typically in late january. Every single year i have ended up stuck somewhere on 40 in a snowstorm, Usually somewhere around NM/texas.
I 10 is a much better bet in terms of weather, but its a little scary. LOTS of border patrol, stripped cars along the road. last year we took I10 into New Orleans, not a terrible trip. Keep in mind, gas is really hard to find on 10 across texas