"The mountain was dangerous in winter."
I am just concerned that "冬の山" can give early learners a misunderstanding of the meaning of the の particle if it gets translated as "in". It makes perfect sense in Japanese, and i to get learners to actually understand Japanese phrasing I think it helps to understand the literal meaning to avoid confusion.
As for the ambiguous time frames, I am not sure I understand not using "に". Maybe it is better to use "で"? For example, "In the summer I play baseball." = "夏で野球をする。" Or would you use に? "夏に。。。"
We're pretty far down the tree here, I think people will have picked up on the usual meanings of の by now!
With prepositions in particular you just have to suck it up and learn that idea x is translated with expression y, and if the closest phrasing in English is 'the mountain in winter' or 'Tokyo at night' or whatever, that's what people should learn.
Duo focuses on technical translation for a lot of grammatical concepts (like expecting certain tenses to show you recognise what's happening, even if another tense is more natural), but for general phrasing it's better to be as natural and accurate as possible. That's what we're aiming for in the end!
Japanese particles do not have equivalent English meanings, that is, they do not equate to English prepositions. "No" in Japanese does not mean "of, by, in, on, etc." It is understood in Japanese by Japanese without reference to however it might show up in translation. (Simply put, Japanese don't have to learn English before they can understand Japanese.)
"No" does at least two things. It marks a noun as being subordinately related to another noun which is the head of it's structure. It can also nominalize a verb but that is not what we have here.
In "fuyu no yama" the "no" tells you that "fuyu" is in a subordinate relationship with "yama". That is, "yama" is described in some way by "fuyu." Since this is not likely a place name, "winter mountain" isn't a very good translation. Of all the possible ways of relating "winter" to "mountain," "mountain in winter" makes good sense.
Apply the same analysis to "watashi no hon" and you get "book OF me > My book. "
Not necessarily. Prepositional phrases in English can be attributive either to nouns or verbs. "Lady in distress, books on the shelf, flowers in (the) spring, etc., " all modify nouns. Conversely, "put on the shelf, plant in the spring, labor in distress" all modify verbs.
Japanese particles follow different rules from English prepositions. の relates to nouns or nominalizes. に relates to verbs. The particles mark grammatical relationships that need to be translated into English according to context and idiom.
Ok, so after reading the comments, it seems that the english translation was huh... 'leading' into another meaning of the same words. That is: This sentences is talking about [the mountain in winter], whereas many of us thought about the [danger in winter] (This for the exersice of translating from english to japanese, by the way). I think I understand well enough my problem but now I have the doubt: How would we phrase this in japanese to say that the danger is the season more than the location? In other words, how do we 'unrelate' the winter and the mountain? I hope this makes sense.