When you go to the Southwest in December, you must be aware of the altitude of the places you intend to visit. Las Vegas, Phoenix, Tucson are all in the low desert regions. Temperatures are likely to be very pleasant and even warm. The South Rim of the Grand Canyon is at a higher altitude. You might encounter cold weather and snow. The North Rim is even higher and will probably be closed due to seasonal snow accumulation.
I have hiked in the vicinity of Tucson, on the outskirts of Las Vegas and in Death Valley during the winter. I would suggest that you consider these options. You can choose to hike through the low desert country, where temperatures are likely to be warm, or you can choose to hike up into the mountains where the air will be cooler. You can even choose to hike near the tops of some of the mountains where you are likely to find snow.
Most tourists go to Death Valley during the summer when the heat is oppresively hot and where hiking without proper precautions can be dangerous. In December, Death Valley is actually very pleasant with nice warm, mostly sunny days and cool nights. That is a great time for hiking in Death Valley.