The correct option is A shut
The tense of a sentence denotes a time, whether it is the time now (present), time then (past) or the time to come (future). The verb of a sentence has most to do with the tense. In the given sentence, we need to fill in a word that determines the correct tense. The speaker performed an action in the past due to the reason "It was cold". Hence the verb is chosen in the simple past tense, as the action has been completed in the past.
Option A: 'Shut' is in the simple past tense in the context of the sentence. It agrees to the sentence in form and meaning, hence option A is correct.
Option B: 'Was shut' is also in the simple past tense, but it's in the passive voice whereas the given sentence is in the active voice. (The passive voice is when the subject receives the action, the active voice is when the subject performs the action). That not being the case, makes option B incorrect.
Option C: Similarly, 'Am shut' is in the passive voice. Also, it's in the present continuous tense, whereas here the action is in the simple past tense. Hence option C is incorrect.
Option D: 'Shutted' is not a word, it does not exist in the English language, hence option D is incorrect.