Hi Pooju, It snows only in the northern Dzonkhags (Districts) of Bhutan. Gasa, Punakha, Bhumthang, Paro and Thimpu experiences snowfall during late December and January. Attached with my comments you can check curated trips by fellow travelers. Please take a look. Thanks!
October to December is the ideal time to visit Bhutan as the air is clear and fresh with sunny skies. January and February are colder, but from then until April the climate remains dry and pleasant and in late spring the famous rhododendrons bloom spectacularly, flooding the valleys with colour.