I read up on this a while ago, and the basic construction while not difficult,is not as straight forward as it seems.
You need a vapor barrier in the walls, but I don't recall whether it should be towards the inside or outside surface. Get it wrong and you can get a build up of condensation inside the walls that leads to other problems down the road..
For our small Roe deer, I use a tall commercial fridge with a fan..Below is a pic of my original unit that cost me some like $70 delivered off ebaybut I now have a slightly larger unit which again I got for next to nothing..
A lot of hunters over here use various old soft drinks fridges..These pics appeared on a British site and show how one guy converted such a fridge..Obviously, you get more room if you use a double door unit.