I have a lot of experience with meat care and butchering, here's what I have come to believe:
1. You do not need to get the hide off of a
deer right away, just hang it in an area with good airflow and prop it open with a stick, and you will be suprized at how quickly it will cool. Now having said that, if temperatures are going to be ridiculously high (high teens and 20's) it may be necessary, but I would be more tempted to leave the hide on and sink the carcass in a cold, clean creek or lake. Now elk and moose are a different story, they will take a very long time to cool down with the hide on, but given cold conditions, ie. around the zero mark, leave the hide on these too (if you can get them out in one piece. The advantages to leaving the hide on are multiple: it keeps the meat clean and moist, the hide actually prevents bacteria and mold from entering the animal (if you blasted it through both shoulders well, they now have another access point), and it keeps the animal a more even temperature, reducing temp. fluctuations, which is good for the meat.
2. If an animal is frozen whole, especially with the hide on, there is no bacteria, et al, in the meat and will present no danger when thawed out and then cut. If the meat has been cut and frozen, then thawed there is a danger of bacteria, that may have been introduced to the meat during cutting, to multiply and become an issue; therefore thaw cut meat as little as possible before grinding for burger. Sausage meat should be kept refrigerated throughout it's processing, until freezing, cooking, or smoking.
3. Cut out all that fat, sinew, and membrane! Especially on deer. If you do, you may find that your wife/girlfriend, or for some of you both, will even eat it. And for Christ's sake, stay away from that band saw!
Having ranted about that, if you are not comfortable cutting your own game and need to give it to the appropriately named 'butcher', then you must remove the hide before delivery....well, that's just one more reason to cut your own.
Ian