Hey Sushant,
I was there in Spiti in August first week and it was fine at night. Only camps in Batal and Chandertal were cold enough to give me a shiver one night. I would recommend you to have one down jacket with you which would suffice all your cold night needs to keep you warm. And also pair of woollen gloves for night with a pair of woollen socks would be an add on advantage.
Happy riding and Happy travelling bro!!!