Hi Prerna! It depends where you're planning to visit in the state of Himachal Pradesh. It is mostly snowy everywhere like Manali, Lahaul, Sissu, Dalhousie. According to weather department, it will rain & snow again on and after 22nd Jan. Snow can impact your travel plans, so you can plan for February there won't be any issue then. All the best.
You can easily go in and out the borders till Solang Valley in Kullu. Even the Parvati Valley and Tirthan are open for all. Spiti is closed and Leh is closed too.