The Best Time to Reach Spiti is September to Mid-October from both the Routes. If you want You can also visit Spiti in winters though what you need to keep in mind that only way possible to reach spiti would be Shimla-Kaza Route. Also you can face lot of road blocks due to heavy Snowfall. But not to say The views would be out the world during this time around the year. Overall It mainly depends upon what kind of experience you want from the valley. In terms of Facilities and Ease of travelling Mid Oct- Sept would be the right time as You'd be able to do a round trip of Shimla-Kaza-Manali. In case You want to experience the White Winter land then maybe Jan-Feb would be the right months for you. It is just You should not expect much from facilities in Spiti valley in these months. In case You want to know more about other Himalayan Valleys and Villages please refer to:
www.wanderworms.com