If you like trekking then here are some of the popular himalayan treks for you during December - January
1) Easy to Moderate - Kedarkantha, Dayara Bugya, Kuari Pass.
2) Moderate - Bhramatal , Har ki doon, Sandakphu Phalut.
If you are looking for a leisure New Year in the mountains, a comfortable place is Mussourie, Uttarakhand.. You will get both snowfall and the taste of chilly mountain breeze as well as the gorgeous Mall Road during the festive season bustling with people and stuff. And if you don't want to stay in Mussourie town you can make your base at Dhanulti (Club Mahendra Resort) a place 15kms away from Mussourie, where you will get quietness, winds howling through the mountain forests and the winter night sky which surely will amaze you. Make a toast to the new year under the stars here!