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!!!