Well as in India, I'd suggest you Uttrakhand and I'm a localite, tourism here is not dwelling so good and very rapid, and I'd love to see people who actually know places here and have travelled. My places for Snowfall will be.
Wan. It is a small village in gharwal Chamoli district.
Munsiyari. Nainital.
Ranikhet.
Almora.
There are many places you can visit. But if you are looking for a short snow trek you can try prashar lake trek or mysterious kutla(few km trek from tosh).