If you want to avoid winter weather in January - stay off I-40. I-10 runs close to the border so the sooner you can plot a course to it, the better off you'll be.
I had a friend in Albuquerque, NM (on I-40) I was going to pay a visit years ago just after Christmas. When I told him when I'd be coming through he recommended I'd be better off on I-10 that time of year. I took his advice. We spent the night in Las Cruces (on I-10) and saw on the New Mexico weather report that I-40 was closed at Albuquerque due to a blizzard that was expected to keep the highway closed for 3 days.
Take I-10 to Phoenix and then work your way north up to Las Vegas over Arizona Route 93 (beautiful scenery!). Avoid Flagstaff because it's altitude is 7000 and prone to snow there too.
If you've got a smart phone, Google Maps and WAZE are too very good free apps you can use for guiding you along your route. Just put in where you want to go on the next leg of your trip (like for gas, to eat or spend the night) and those apps will get you there.
If you want to use paper maps, they're still available at the welcome centers on the interstates.
