Hey Ranjani, you have these treks to take in January:- Nag tibba in himachal pradesh Prashar lake in himachal Pradesh Kuari pas Trek in uttarakhand dodital Trek ... Chopta and chandrashila lake Trek in uttarakhand ... Happy Trekking!!!
Har ki dun trek is a good option.
you can also plan for chopta trek in Uttarakhand and nag tibba trek best way to check for upcoming treks and other knowledge on trekking visit INDIAHIKES website in which you can get great help. other treks to be considered 1: Phulara Ridge trek (easy level)
5-6 days 2: Dayara Bugyal trek (easy -moderate)
5-6 days 3: Chadar trek - frozen river zanskar trek
It's all about the weather. Trek per se is not hard but negative temperature makes it difficult. If you don't become cranky in cold weather and you have done any one-day treks before then you can go for it.