As a reader, theme is very important to me. This applies to novels and short stories and I find that all of my favorite writers are writing about things that mean something to me or about issues and ideas that I think are both relatable and significant.
With this is mind, style becomes a vehicle for theme and the question becomes, "Does this style convey and support important and compelling themes?" In my opinion, Hemingway's style is usually in line with his thematic and artistic interests. His protagonist is always at odds with himself. There is almost always an inner schism that is suppressed. This take on a person's internal life is fascinating.
The attention to details of food and drink and how much snow was on the mountain serves to distract and suppress and evade the real, emotional concerns of the narrative in ways that, I think, help to clarify and demonstrate the themes he is working with (a tendency to be romantic while disliking romance; a willingness to love and a hesitency to take overt emotional risk, etc.)