Hi Harman, If a valley covered under a thick sheet of snow is on your mind, then you must go in January or February. For lush green hills, you must visit in August. If the colors of autumn interest you, then plan it by late September or early October.
The roads are open throughout the year for Spiti Valley.
If you want to see the Snowfall, the best time would be February or March. It is a very beautiful place and it totally depends on you how you want to enter the heaven :)