If your going to keep it on ice I would not wrap it as long as the ice/ice chest is clean, you want the fluids to be able to drain away from the meat not be held next to it.

In my opinion this is not aging though, its bleeding it out. We don't do it.

14 days is a long time. I only feel comfortable with 7-8 days on ice as long as its kept full of ice and constantly drained with the plug open. I'm sure others do theirs longer. I also don't think its a good idea to put it in plastic bags. When someone says don't keep it wet they mean don't let it sit in water. Good layer of ice on the bottom and on top with the drain plug open and cooler tilted towards the plug side (put something under one end of the cooler) and you'll be fine.

I quarter them out and put in a cooler with bagged ice (not opened) and drain the water/blood every day for a few days.
I generally will do this for 3-5 days dependent on my schedule and then bag and put in fridge for up to two weeks for aging. Meat is always delicious, tender and with no gamey taste.

Right now, on my deck is the quartered out deer my son shot last Monday.
With it being so cold the ice has barely melted, I drain the blood out every few days.
I need to debone and then will have it turned into sausage.
I will probably just freeze it and defrost when I am ready to take to processor.

Do you bag it in a regular zip lock bag when in fridge?

my mother hung in a potato sack on the poarch until greem mold formed and then sliced trimed and fried. could cut with a fork. keep in shade. Will keep for weeks.