I went in November and it was pretty cold. So December will be very cold, especially if you start for the darshan in the night. The temperatures can really drop mid-Dec.
Vaishno Devi Yatra is open throughout the year for pilgrims and tourists. However, the best time to visit Vaishno Devi is from March to October. from November to February, Vaishno Devi witnesses sub-zero temperature. So, until you're physically fit and a snow enthusiast, winter season is not recommended for a visit.