Ya know, what can you do when it is poring down on the Wet side?

Things are going to get wet it is hard to prevent it. You do the best you can with what you have. If it is raining the chances are your animal is going to be wet to begin with.
Heat and Moisture are what bacteria need to thrive. They work faster in these conditions. When an animal is killed it needs to be kept cool and dry until 3 things can happen;
* Either you get it into a freezer,
* Get it to the taxidermist,
* Split, flesh, and salt the cape correctly.
For bacteria to stop working the cape either has to be completely frozen solid or the cape has to be split, fleshed and salted and the moisture content of the hide brought somewhere bellow 15%.
I suggest carying a couple dry towels with you if you are going to be hunting in the rain. They do not have to be on your person but in the truck. When you get the animal back to the truck dry the cape off as best you can and either get it into the freezer ASAP or to the taxidermist ASAP.
You can also carry one of those cheap ponchoes with you. The one thing you really don't want to do is wrap that warm cape up in plastic but you can lay the poncho over the cape enough to keep it from getting soaked. Best place to put a wet cape for transpot is in a cloth game bag. It allowes the moisture to drain off along with blood and body fluids. In plastic a wet cape is going to sweat and become a bacteria feeding ground.