Hey Niwedita, You can celebrate new year in camps on snow mountains. You can go to following places for camping : 1)Kheerganga trek(One day trek, Parvati valley-Tosh, Malana, Kasol) 2)Triund trek (One day trek, Dharamshala-Naddi, Dalhousie, Macleodganj) 3)Prashar lake trek (One day trek, Mandi) 4)Kedarkantha trek (5 days trek, Uttrakhand-Dehradun, Rishikesh, Mussourie) Hope this would help you.
The most nearby, economical, peaceful place to spend your new year near delhi is to stay at a camp in Rishikesh. You will love it and if you are an adventurous freek then try rafting the next day in that chilly water. All the best!!!