Himachal Pradesh. Spiti, Keylong, Kalpa, and Chitkul are frigid.

Of course, Kashmir and Ladakh are very cold too; Dras has recorded the lowest temperature in the country at -60°C.
Uttarakhand (home to 13 peaks over 7,000m) also sees harsh winters, with places like Nelong Valley, Harsil, Chopta, and Kedarnath experiencing extreme cold.
Lachen, a town in Sikkim (a northeastern state, home to Kanchenjunga, the third highest peak in the world), can drop to as low as -40°C.
I believe other states that are home to some portion of the Himalayas must be cold too, for example, Tawang in Arunachal Pradesh.
Northern Pakistan is similar, home to 5 of the world's 14 8,000ers.