"The cat closed the fridge door." would be the most natural way to say it in English. 'the door to the fridge' is the next best. 'the door of the fridge' sounds a little less natural than 'the door to the fridge' - HOWEVER, it is still grammatically correct and a native speaker might say it, so I think Duolingo should allow it.
I wrote 'The cat closed the refrigerator's door' and marked wrong. Do we have to be an expert in English language or master the English language in order to learn Spanish on Duolingo? They should find a way to encourage us learn Spanish who are not native English speakers, otherwise when we find these English translations marked wrong for petty errors, we lose our zeal (it's my opinion, don't know if others would agree). Thank you!
"Freezer" is "congelador". There are lots of different terms for "refrigerator", depending on what country you're in, including "nevera". You can find some others in this thread: http://www.spanishdict.com/answers/245734/whats-is-the-difference-between-la-nevera-and-el-frigorifico