Does sleeping in a cold room burn calories? can it also make us lose muscle mass?

Yes/no: Simply sleeping in a cold room won't burn any more calories but shivering will. However, you probably won't be able to sleep if you're shivering all night and you could get sick. Muscle mass won't be affected by sleep alone.

Not much.: Your body is constantly burning calories, that is the BMR, basal metabolic rate. Does the BMR increase in a cold room? If you are shivering, then certainly. There is a significant muscle building during sleep, not muscle loss.

Calories burned: You burn small amount of calories when you sleep. Less than when you exert yourself or are awake. Unless you are actively shivering you won't likely burn more calories in a cold room than in a regular room. You generally burn more calories in a warm environment. If you don't actively use your muscles you will lose muscle mass. Best way to burn calories and maintain muscle mass is exercise