First, learn to mistrust the answer key to your exercise book. It's wrong. Both sentences are correct, but they mean different things. In general, learn to mistrust English textbooks that only provide correct answers without explaining why others are incorrect; they tend to be written by people who don't know English well, and they often have strange ideas about how grammar, and English, work.
Second, there is no "possessive case" in English. English nouns have no case. The possessive suffix -'s (technically the English inflectional morpheme {-Z₂}) is not a case (cases are always attached to nouns), but rather a noun phrase clitic that attaches to the last word of a noun phrase. That includes
- the Minister of Foreign Affairs' speech.
Third, you're right that the relation between snow depth and snow's density is confusing. They're two different constructions, with different affordances.
In the noun compound snow depths, snow is referring to the multiple measurements of different events of snowfall, as shown by the fact that depths is plural. This is equivalent to depths of snow, as in
- The snow depths/depths of snow in this location are quite unpredictable.
Similarly, rain depths refers to multiple depth measurements of individual rainfalls.
But in the noun phrase (not noun compound) snow's low density, snow is referring to generic snow, not to an event of snowfall. It says that snow -- all snow -- has a low density. It means the same thing as the low density of snow, as in
- Snow's low density/The low density of snow is due to its crystalline structure.
Fourth, as to *snow low density, you can't say it because it's ungrammatical. You can't combine two nouns with an adjective sandwiched in between. The only thing that can come before the adjective in a noun phrase is a determiner, like the low density, its low density, or snow's low density. Possessives are determiners, you see.
Fifth and finally, snow's depth is grammatical, but wrong in this plural context, because both snow and depth are singular, so snow has to refer to a generic measurement applying to all snow, instead of referring to individual measurements of individual events.
A complex question, involving a lot of complex phenomena. But don't believe everything you read in English textbooks.