First moose I got, it was 40s at night and 60s during the day. Shot it early in the hunt so it hung for 7 days before we could get out and then processed it once we got home. I think it was 8 days from kill to freezer. Shot a moose in the arctic one year in late September and it was about 15 every night and 40s during the day and it was about 10 days from kill to freezer. This year's and last year's animal were cut up within 72 hours of the kill which were early august kills (uppers 20s at night and mid 40s during the day). I didn't notice any difference it any of them moose. All big bulls.
You will likely turn most of it into burger. For the cuts that are not burger, I take them out of the freezer 5-7 days before I plan to eat them and place them on a wire rack in the fridge, sprinkle generously with rock salt, and loosely cover them with tin foil for the week. That will get most of the blood out and I think makes them cuts much more tender (and the wife claims in removed the game flavor). It's all personal preference. Most people don't have a climate controlled space to hang meat for that long. If I did, or if we take an animal and the weather allows that I can let it hang or rest on a pallet for a few days, I usually do.
The family business growing up was a custom butcher shop. We'd let a good number of beef hang for well over 60 days if the client requested it. Literally would be cutting off the outer inch or two all around the animal and throwing away the green and white mold. I never noticed a real difference in any of them compared to something that hung for a week. We only accepted grinder-ready wild game. Most of it was covered in dirt or hair and disgusting; which is why my dad never hunted an animal in his life.