[Post two of the above answer...I hope.]
In paragraph two, we learn that the ones who don't go to war anymore, even though it is "always there," are wounded soldiers who take daily trips to the hospital for treatment. First, we learn that there are three routes to take to get to the hospital, which can be associated (maybe Hemingway should not have protested so much about not using symbols...) with choices. We then learn that each of the three routes leads to the same bridge to cross and the bridge leads to the one and only entrance and that entrance opens to the one and only exit. In reality, the three routes, or choices, are the same route and the same choice, with different scenery and experiences along the way, one of which is a warm human exchange with the lady who sells warm chestnuts. We then learn that in the courtyard there are funerals everyday. This fact calls to mind what we've already read about the game that hangs before the shops. Hunted foxes and other game don't need funerals; their deaths serve useful purposes. Noble deer and innocent song birds remind us of the emptiness and twisted uselessness of some deaths. These associations in juxtaposition to the funerals at the hospital everyday betoken Hemingway's theme: Human deaths lead to funerals. Human deaths don't lead to useful purposes like autumn game used for super. When humans are hunted as in war, which is like a cold wind from the mountains that is always present and blows everywhere, their deaths are as heavy and empty as the death of a noble deer and as senseless as the death of a song bird. [I am not exactly a fan of Hemingway, but this is impressive craftsmanship, symbolism absent or not.]
[This answer is too long for one post and so is in two posts...I hope.]
Part of Hemingway's aesthetic of writing (philosophy of the art of writing) was to emphasize sensory detail. Another part was to use the common place along with mundane experience, which are commonalities to generally all people, to point to deep philosophical questions of life. And he did this by using deceptively simple language. If you look closely at the words of the first two paragraphs of In Another Country, you will see that, in general terms, every third to fourth word (sometimes every second word) is a sensory word or a word that indicates associations with well known experience or physicality, like time and place. For instance, let's use this sentence: "It was cold in the fall in Milan and the dark came very early." A quick analysis renders this description: "It was cold (tactile) in the fall (time; tactile) in Milan (location; sensory associations: smells, sights, activities, memories, etc.) and the dark (visual; tactile; time) came very early (time)." This same sort of analysis can be applied to the sentences in which Hemingway discusses the "game," which is a word loaded with associations itself, which every hunter relates to: time, tactile, sounds, sights, smells, physical sensations, locations, psychological impact etc.
When Hemingway talks about the game hanging, his tone is that of relaying a pleasant experience, light, smiling. He surrounds the game with "pleasant" experiences of electric lights, looking in shop windows (window shopping), walking along the town's streets (an evening stroll); snow lightly powdering sprightly little fox tails that blow in the wind. His tone is not distress...until the deer come in. Deer are larger and commonly considered noble beasts with eyes that some hunters say look right into your soul. For the description of the deer, Hemingway's tone changes. The deer are "stiff and heavy and empty." The small birds, an association suggesting song birds, hang in the wind and seem to twist in the wind, in a different manor from the foxes tails that seem to fluff about in the wind. The passage is capped with a repetition of the cold fall and the wind (mentioned directly or indirectly six times), but this time Hemingway adds that is blows "down from the mountains," a literary convention representing adversity and stark circumstance.
Hemingway is using this meticulously crafted passage to setup a profound association with the second paragraph and to lay out his theme. Sentences 1, 2, 3 and 4 of the first paragraph establish a light hearted association with hunting: animals may be hunted because animals that are hunted become welcome food or other provision with which to sustain human life. Sentence 5, about the deer, plays upon the accepted idea of the nobility of deer and thereby establishes an association with noble humanity (Hemingway protested the suggestion that he employed symbolism, but it is clear that he made extensive use of association of ideas), also associating the emptiness left within when they are hunted with the nobility humanity.
[Post two of the Answer follows below...I hope.]