We were at Chaco Canyon the last weekend of September last year and it was down to 28 degrees overnight in the high desert. But it warmed up quickly with sunrise and the weather was spectacular during the day.
The following weeks it was a bit warmer in Taos, Abiquiu, Santa Fe, Albuquerque with chilly nights, gorgeous days. The Balloon Fiesta weather in ABQ is known for being quite cold at dawn during the launches.
So just be sure to have what you need in the way of propane for your furnace, a space heater for hookup sites, and warm clothes in layers you can shed.
There's a good COE campground with electricity in Abiquiu, by the way, at Riana Lake in the heart of scenic Georgia O'Keeffe country.