Re: Nashville to Kansas City to Oklahoma City to Palms Springs CA.
You're right about the weather on I-70 vs. I-40, though I-70 through Western Colorado and Utah is definitely a spectacular scenery ride. The I-40 trip is probably easier this time of year and there are some nice views their too. You'll definitely burn less gas on I-40. If it starts snowing on I-70, you may need chains or have to go real slow.
If you want to spend more time in Palm Springs, I'd go I-40. If you have the time to enjoy the ride, I'd go I-70.