Welcome!
How many days do you have to make this trip?
The best last minute advice on which routes to take will be online at the various states' DOT websites and the Weather Channel. Right now, the weekly planner for this week isn't looking too good.
I would get a set of tire chains if you don't have any. Cable chains are sufficient. Without them, you may be delayed and have to wait out a storm (actually, that wouldn't be a bad idea anyway). California in particular is quite picky about their chain law, and if you are going to be living out there and want to go into the mountains in the winter, you must carry them.