A HRTC bus runs from the Reckong Peo bus stop in the morning ( departure 7AM) and reaches Kaza around 6 PM. No public transport exists in the Spiti valley in winter so traveling by own vehicle or shared taxis are the only mode of transportation. Walking on icy roads.
You can reach Kaza through Reckong Peo in a HRTC bus and come back the same route, as Kunzum pass and Rohtang pass are closed in winters. But going around Spiti through public transport isn't possible. You may rent a bike from Kaza market but I'm not so sure about driving bikes there in winters. Best you can hope for is to meet people who are traveling in cars and can give you a ride. Hitch hiking basically.