I think you'll be fine.
It's possible that there will be snow and freezing weather in the local mountains that you'll have to pass. But any kind of chance of an actual wet/frozen road is fairly slim if you're driving during daylight hours. And it only takes about one hour from the desert floor to the warmer coast if you go down through Phoenix to Yuma and out Interstate 8. If you can make it to Phoenix without winterizing I don't think you'll need it after that.
You could also take the 10 through Riverside and probably only see about the same amount of snow.
Make sure you bring a heavy jacket with you because it can get down into the low 50's and sometimes 40's at night around here. ;)
