I try not to let my venison sit for more than a week. I put my venison in a bag and put it on ice. I know several hunters who put their meat directly into the cooler with no bag and lots of ice and water. I don't like the meat resting directly inside the water. But it stays cold.
No water touching any red meat. This makes for dry meat. Fish an chicken I freeze in water. I bag my venison and use frozen milk jugs to keep cold. I process my own including grinding and sausage. I have one lease mate that thinks it is ok to hang deer in shade at 60 degrees. Not me. I don't even field dress. I hang, skin, dump guts in bucket and quarter almost immediately.