A sentence is in active voice when the subject is the doer of the action.
A sentence is in passive voice when the new subject (object in active voice) is the receiver of that action.
In the given sentence, "During the cold and foggy afternoon" states a period of time. Hence the tense of the verb must be in continuous form.
Option D: 'Were being sung' is a passive verb form in the past continuous tense. The passage narrates past events and requires a past continuous verb form (passive). Hence option D is correct.
Option A: 'Were sung' is in simple past tense (passive). Since a period of time is mentioned, the action of singing is a continuous one. Also, simple past tense is used when the action is short whereas here it takes place during a course of time: "afternoon". Hence A is incorrect.
Option B: 'Have been sung' is in the present perfect tense whereas the sentence is in the past. Hence B is incorrect.
Option C: 'Is' is a singular verb, whereas the subject 'carols' is plural. Also, it's in the present continuous tense. Hence C is incorrect.