Definitely you can give a shot to Himachal Pradesh or Uttrakhand. Enjoying the winter around the snow capped mountains is of different level. Just quickly book a flight to Delhi and :
Option 1 - take a overnight bus to Kasol and enjoy your holidays living like a Nomad and going for amazing treks nearby.
Option 2 - take a bus to dehradun, then go by shared taxi to Dhanaulti and have leisure time in the mountains. Also you can enjoy the adventure activities in eco park of Dhanaulti
So many options are there but since it's Christmas time, you will have to be prepared to find crowd. if you are ready to explore and experience extreme cold, then visit any hill station in North India; if not, then i would suggest going to Rajasthan (Udaipur, Jaisalmer, Jaipur etc) or any costal area in south india. For good places to stay, i would suggest you book in advance since it is a holiday time.