Rather than freeze initially I would refridgerate first, meat does better when it is aged for a while, the best is to dry age the second best is to wet age. 5 days in a Fridge will do wonders for its tenderness. Many domestic freezers here have a thermostat which allows them to operate as a fridge.
For the same problems you probably envisage we have taken to slaughtering on site which means that effectively we get rid of the large masses of bone which takes up so much space. We cut and package our cooking meat, cut strips for jerky and then all the offcuts are set aside to make sausage or ground meat. We grind the meat on site as well. All this goes into freezer bags (vacuum pack if you can) and then into the fridge for 5 days to wet mature. It then is placed in the freezer pretty much fully processed.
I had considered making a refridgerated trailer but we have never had a problem with meat. Remember unlike a steak which has already been hung at 5 deg C for about 2 weeks your venison is fresh.
It is generally not good practice to refreeze meat, it toughens it and causes other unwanted problems. If you can rather keep it at 3 - 5deg C and then freeze post processing.
The trick will be to field dress ASAP, hang to bleed it animal out and then get the temperature down real quick. One way is to quarter as you suggest. You can use what we call "mutton cloth" here to place the quarters into but remember that a fridge and freezer dries meat out so placing into mutton cloth and into a fridge will effectively allow you to dry age (the best) but this also result in meat loss as the outer crust becomes unusable. Do not be tempted to use large garbage bags due to the size of the joints. Many of the bags are treated with agents that are not good for us, they are after all for garbage. Only use food grade bags. Meat hates being in plastic although it is a necessary evil.
Lamb in mutton cloth.
From a recent hunt in South Africa.
Getting towards then end of one carcass hunted two weeks ago. Note the near half full Coleman. The meat had been hung for 3 days already at 5 deg C, we were butchering at about 25 dec C (about 80F) and the meat then was packed into freezer bags. Transported back home in Colemans (trip 7 hours at 25C). The meat then spent another 4 days in my fridge before I made the jerky and froze the other.
Hope this helps.