Hey Gaurav, December is off season for tourists in Leh so there will be not many hotels open at that time. So make a prebooking before going there. You can search hotels on Oyo,Make my trip or Trivago.
Hi Gaurav, i'm attaching with this comment some hotel options for you in Leh ladakh. You can click on them to find detail about the hotels and also use the same link to book them.