Hey Deepika, Spiti is a magical wonderland that you HAVE to visit! However, December is definitely not an ideal time, especially if this is your first trip there. By December, all of Spiti is covered in thick snow and has sub-zero temperature. To give you an idea of how bad the winter there is -- the water freezes in the pipes, you have to use dry toilets located outside the homestays, there is usually no electricity and hot water is available only for essentials. In case an experience of the harsh winter is what you're looking for, then you can surely head to Spiti, but even then, I would suggest that you book with a tour operator, in order to make things easier for you. If not, then it is best to wait it out till next year and visit anytime between May - September. Hope this helps!
Happy travels :)
Via Simla one can plan throughout the year unless you want to travel via Rohtang pass. You can reach to Kaza via tabo and nako and come back same way. However, winter months roads availability can be unpredictable