Some great places to explore in January would include Khajuraho, Corbett, Shimla, Jaisalmer, Nainital, Kalimpong, Jaipur, Udaipur, Manali, Dawki, Goa, Chamba and trust me this list goes on because the winters are great to explore everything around our nation. Here is an article that talks about more places you ca explore in January: https://www.tripoto.com/india/trips/best-places-to-visit-in-january-in-india
First you should pick the area ,state ,direction etc. like northern, southern, eastern, western India is such big country. you should be specific about which part of country you looking for.
In hill station for snow: auli, chopta, Lansdowne, dhanaulti, gulmarg, pahalgam, kufri, narkanda
other places: Jaipur, hampi, munnar, Jaisalmer, gokarna, udaipur, kochi, Ooty, Alleppey