Is it permissible to spend the night in the car in Muzdalifah due to the intense cold, and is it permissible to depart from Muzdalifah after midnight?

The scholars have agreed that staying overnight in Muzdalifah extends until Fajr for those without valid excuses, and this is what the Prophet, peace and blessings be upon him, did. Staying overnight in Muzdalifah is obligatory according to the majority of scholars, though they differed on the minimum required duration. Most scholars are of the view that it is achieved by being present in Muzdalifah after midnight, even for a moment, regardless of the person's state (asleep, awake, riding, reclining), and whether or not they have a valid excuse. This is the madhhab of the Shafi’is and Hanbalis. Based on this, it is permissible to depart from Muzdalifah after midnight, even if the person does not have a valid excuse, though it is preferable to remain until morning. There is no harm in sleeping in the car.