Spiti valley is accessible in April. It is the start of tourism season. You could try covering Chitkul, Naka, Mud village, Kaza, Sarahan and Shimla. The weather is chill though not cold. You could plan visiting Chandratal, Pin valley. Trekking is popular in this valley, along with camping, which you could prebook.
https://www.tripoto.com/himachal-pradesh/trips/20-interesting-facts-about-spiti-valley-you-should-know-5f155fe973bae
Kindly check the above Tripoto link for more details.
Spiti is accesible throughout the year. april is the season where the snow starts melting. u will defntly find snow there. but u wont be able to cross kunzum. i was there in june and could only reach kunzum top but cudnt cross it