One important thing to remember is that altitude counts. While in many places in the U.S., you can go north to get cooler and south to get warmer. But out west and in some other places, there are high places in northern Arizona and northern New Mexico that are high and very cold in spring and fall. For example, you can ski in Santa Fe, NM, in March. And many of the national parks in Arizona and Utah can be very very cold in winter, even though they are supposedly "southern" states. Phoenix may be very pleasant in January, but head north to Flagstaff, and you will encounter snow at those high elevations!
In a personal example, I was once staying in Las Vegas in February and had made reservations in the mountains nearby. I called to ask about cell service and then asked about the weather. I was shocked to find out that they were skiing there!! It was about 70 in Las Vagas but in the low 30s in the mountain campground and even colder that night!!