What do you guys do with your deer in the hot weather, hang in cooler, butcher right away or what? Some even say they soak then ice water.

You gotta get it cooling quickly.  However you can manage that is good. I tend to stuff bags of ice between rear legs and inside chest cavity, wrap in a tarp and then bone it out the next day, putting meat into gallon or two gallon bags on ice.  That buys me several days to butcher, clean and wrap.
CHuckC

Best thing I found was a big cooler that they use on charter fishing boats. Imagine a Yeti that you can lay two deer in. Keep bocks of ice frozen and your set until you can work up the meat.

I hunt around home so I bring it right home, skin it out then get it quartered up and in a cooler.

I skin and quarter asap putting the meat in an ice chest. I run the cooler full of tap water and continue to let it overflow out the top and flow from the drain plug in the bottom for several minutes while occasionaly stirring the meat around with my hands. I have found that this not only cools the meat but also rinses off most of the excess blood and any hair left on the meat floats to the top and runs over the side. After that i drain off all the water then pour as much bagged ice over the meat as the cooler will hold. Pour some water over the ice slosh the meat around to make sure ice and water get in between all meat and let it sit. If you drain the water and add more ice daily you can keep it like this for up to a week before processing and freezing. The key is to drain the old water and add new daily. (Disclaimer) I have chlorinated city water and i believe this helps keep down bacteria that will cause meat spoilage. Well water might not allow you to wait as long to process the meat.

Dress, skin, quarter and in cooler with ice as soon as possible.

I always thought water on the meat before freezing would cause bacteria to grow.