"A mountain in winter is a dangerous place."
ところ means place.
If you don't have ところ it would be 'a mountain in winter is dangerous.'
Perhaps they decided it was close enough. Sometimes if there is only a small discrepancy Duo lets it slide.
It's still not accepted now. I have reported it too. Duo also doesn't accept ”冬” and ”危ない”.
Because the subject is the winter mountain, the は comes after the mountain. You wouldn't be able to have two はs in a sentence like this. There is only one subject.
We cannot use に because it shows direction or action. i.e. ふゆに山へ行く。I go to the mountain during winter. The example sentence is a statement and isn't showing action.
The の shows ownership. The winter's mountain. That way they can be connected.
There are other ways to mix up the sentence to say the same thing while using different particles. But this sentence needs the の .
We often say things like this:
夏(なつ)の海(うみ)はきれい。 The ocean during summer is pretty.
秋(あき)の紅葉(もみじ)は美しい(うつく)。 The autumn leaves are beautiful.
What is a "winter mountain" though? The mountain is always a mountain, and the English certainly doesn't reflect anything like that. I got the sentence in Japanese first, but if I'd had the English I would have probably translated it to something like 冬は山があぶないです
It does. Just like you can say rainy mountain in English, you can say winter mountain, summer festival, spring break. If you write 冬は山があぶないです it would translate roughly as "In winter the mountain is dangerous". The point is winter, not the mountain. See where it's wrong?