You can travel all the year. best time March to Separate .
but you want to feel of -20*c and enjoy the White Spiti landscape then plan after September to February end. in winter it's good for wildlife photography and 4x4 snow drive experience.
Best time to visit Spiti valley is during June and September month. In this period one can travel a full circuit of Spiti i.e. Shimla to Manali via Kinnaur and Kaza. Here is a itinerary for Spiti valley circuit tour. https://raachotrekkers.com/spiti-valley-tour-package/