Here's how I would handle a deer in those circumstances. First rinse the cavity with cold water to remove any excess blood and debris. Then hang it field dressed head down in a shady area where the wind would still get to it, fill the cavity with three or four bags of block ice (it holds longer.) If it was evening when you got it, leave it overnight with the ice in it, or if it was morning leave it until evening of the same day.Next skin it ( It should feel cold to the touch under the hide.) and rinse the outside with cold water. Quarter or break it into appropriate primals. Put a layer of ice cubes in the bottom of a cooler and place half of the venison on top, add a layer of cubes on top of the venison then the second half of the venison with more cubes on top of that. Leave it for 10-12 hours to througly chill the venison, then take and dry the primals/quarters and place it clear plastic bags. You can fold the ends of the bags over withoiut sealing them. Drain any water that may be in the cooler and save the ice. Put the primals on the ice that's left (or add some if needed) top them with fresh ice (block if you have it.)Don't allow the venison to sit in water. If water accumulates, then drain it and add ice. If moisture appears to be forming on the venison or the inside of the bag then pad the venison dry with paper towels and open the ends of the bags. Try to keep the open ends up in a way that the melting ice won't flow into the bags.You should be good for a few days this way. The biggest key is to get it chilled all the way through before putting it in the bags.

Good luck,Dave & Ruth