April–May and September–October are the best months. Daytime temperatures are mild, nights are crisp, and the dirt access road is most likely to be passable. Summer is hot — over 35°C is common — and afternoon thunderstorms can turn the road to mud in minutes. Winter brings real cold at this elevation (1,900 m) and snow can close the road outright.
The Chacoans built precise alignments to the sun, and the park makes a feature of them: at the summer solstice the visitor centre and Pueblo Bonito host dawn programmes, and the equinoxes draw smaller crowds. If you are timing a visit around an astronomical event, book the campsite far in advance — it is the only accommodation inside the park.